The driving force of both works is that a man lost his beloved (Christine for Strange, Ying Li for Wenwu) and felt responsible, thus driving them to try and "undo" the death somehow—Strange through trying to gather enough power to break an Absolute Point and save Christine, and Wenwu through getting to Ta Lo and rescuing Yang Li (even though she isn't actually imprisoned and really is dead).
In both cases, the man in question fails and it costs him his life. The main difference is that Strange doesn't stop in time and dooms the entire universe, while Wenwu, after realizing that Ying Li is gone, passes the Rings onto Shang-Chi so that he can save the world from the Dweller-in-Darkness.
The Arbitrary Skepticism of Shang-Chi and Katy's friends at the end, while understandable, seems kind of weird when you consider that the people of the MCU should know about things that are just as outlandish as what the two of them described—after all, Norse mythology has proven to be real, aliens invaded the planet, and half of all life vanished into dust. A possible reason for the skepticism (outside of thinking that it was made up in response to Soo telling them they had so much potential) is that the story itself takes place on Earth, and most of the more outlandish stuff that happens on Earth came from other realms while this apparently happened in a secret area on Earth itself.
In addition, it's less that they're skeptical of the events themselves, just that loser valets Katy and Shaun were involved in them. In all likelihood, it's probably very common for people in the MCU to claim they were somehow involved in some big superhero battle for the fate of the planet in order to appear more cool.
The weirdest part is that there's a viral video showing that they were in fact involved in some strange MCU stuff, so they should at least believe that Shaun is great at martial arts and involved in something.
In The Stinger, Wong brings Shang-Chi and Katy to what is most likely the Sanctum Sanctorum. It might be wondered why it's him and not Doctor Strange, but Spider-Man: No Way Home reveals that Wong is now the Sorcerer Supreme and not Strange.
Why didn't Kamar-Taj detect the Ten Rings until the end of the movie despite it being in use for a millennia? Xu Wenwu used them only on a small scale as a personal weapon. Meanwhile, Shang-Chi used them to destroy a giant soul-sucking demon in a huge explosion.
It's also very likely that the original owner was a pure muggle while Shang-Chi has inherent magic from his mother that gave them an extra oomph.
The source of the postcard is never outright stated, but in retrospect, it's obvious Wenwu sent it. He intended for the siblings to reunite due to the postcard and send them a message: "I knew where you both were the entire time."
Wenwu's interest in Ta Lo was depicted as him seeking more power, but with the reveal of the Dweller, it takes on a new angle. It's possible that his initial attempt to reach Ta Lo was motivated by the Dweller promising the one thing Wenwu wanted: More power. Except that when he met Ying Li, Wenwu found something he wanted more than power, and the Dweller lost its hold on him. After she died though, the Dweller started whispering to him again which is why he was already looking at the legends of Ta Lo before he heard Ying Li's voice.
The Eternals trailer seems to indicate the Blip awakened previously dormant Deviants. If that's the case, it's possible that the Dweller was actually weaker before that and thus only able to subtly influence others to do its bidding. After the Blip, it gained enough strength to more directly contact its pawns, which is why it took so long to begin whispering in Ying Li's voice.
Considering how hard Wenwu snapped back to his Ten Rings persona after the tragedy, it shouldn't be surprising that he also returns to a Stay in the Kitchen attitude. He's a thousand-years-old Chinese warlord, meaning he grew up during the Song Dynasty which saw the rise of Neo-Confucianism.
The real Ten Rings organization took the trouble to break Trevor Slattery out of a US federal prison, just to bring him to their leader to personally execute him for his 'mockery'. This makes more sense given how Wenwu lost his wife. When he'd retired to be with her, he lost the fear-endowed respect of even low-level criminals like the Iron Gang, which was why that gang could dare to invade his home and kill his wife. Because of that, he would be compelled to punish any form of disrespect to his name, especially one that had appeared in international papers.
Wenwu sparing Trevor, instead making him his jester of sorts, can be also be attributed to his time with his wife changing him for the better. So he just made it seem like he punished Trevor to send a message without actually killing the man. And even if his enemies find out he didn’t kill Trevor, finding out he made Trevor his personal jester would make it seem like Wenwu wouldn’t just kill his enemies, he’d humiliate them too.
There's a sense of irony to be had when the gang that pushed Wenwu to go back to his old ways is named the Iron Gang, much like how the Ten Rings pushed Tony to become Iron Man.
Notice Shang's hands when he uses the Ten Rings to defeat the Dweller-in-Darkness. One hand is open and the other is closed, representing his mother and father, respectively, as well as the many concepts associated with them.
The Ten Rings sparing Trevor Slattery and making him their court jester because they found his hammy performance of Macbeth to be Actually Pretty Funny makes a lot more sense when one realizes that China has historically adored Shakespeare since the 1980s. And having a form of free entertainment by imprisoning a guy who knows his work incredibly well is just too good to pass up.
Why does Trevor know Shakespeare's works so well? Because he's a failed actor from England. One of the Royal Shakespeare Company's stated goals is to train the next generation of talented actors and other theatrical talent. Many internationally famous actors got their start by joining the company, and others have gotten famous by acting in Shakespearian adaptations. Trevor likely joined or tried to join the company in an attempt to mimic other actors' success stories, and learning Shakespeare would demonstrate his skill at line memorization and make him more likely to be cast in a Shakespeare-derived work.
Given Strange was gone for five years, Wong may owe him more than one tuna melt.
Plus, without Strange to look after once he was gone in the Snap, Wong decided to find some new friends and make a name for himself. Doesn't matter if it was in such shady conditions.
Wong also seems to be on friendly terms with Abomination, referring to him as "Emil" and indicating they've been working on his anger and aggression issues. Wong isn't just cage fighting for profit, he's trying to make one of the most dangerous physical beings on the planet less of a threat. Perhaps in time, thanks to Wong's tutelage, the Avengers will finally recruit Blonsky.
She-Hulk: Attorney at Law provides the answer: Wong was actually training as the Sorcerer Supreme, and he broke Blonksy out of prison that time only just to test his strength. And considering Banner made a device that reverts him back to human form, Wong probably wanted someone who was as strong as the Hulk, so he went for the second-best alternative: Blonsky.
Katy betting against Shaun in his fight is actually a clever hustle on her part—if he loses, she wins by betting against him and if he wins, Shaun gets a huge payday as Jon-Jon pointed out (that he would of course share with his best friend). Either way, she gets paid.
The animals in Ta Lo represent specific concepts:
The Great Protector is a Chinese dragon, a symbol of divinity and authority.
The Chinese guardian lion represents peace, supremacy, energy and happiness.
The quilin represents longevity and prosperity.
The fenghuang (phoenix) represents immortality.
The hulijing (many-tailed fox) represents supernatural powers, peace and prosperity.
The Dweller-in-Darkness is its antithesis and represents darkness and corruption, which fits Wenwu.
The dijiang (Morris) represents chaos and confusion, and enjoys singing and dancing; an appropriate animal to befriend the actor Trevor Slattery.
The MCU film that receives the most references in this movie is Iron Man 3. A most likely unintentional one is between that movie's post-credit scene and this one's mid-credit scene, which both feature Bruce Banner with a surprising note regarding him. In Iron Man 3, the twist is that Tony has been telling the story of the movie the whole time to Bruce, who fell asleep at the start and seems relatively annoyed but not angry when Tony launches into another story from his past as he recognizes that this is just who Tony is. Here, the twist is that Bruce is back to being normal Bruce as opposed to Professor Hulk from Avengers: Endgame. Second, when Carol gets an alert, she tells the others that she has to leave and Bruce has her number if they want to get in touch. Bruce says immediately afterwards that no, he doesn't have her number and she does stuff like that, showing annoyance but no anger because he recognizes that is who Carol is.
It seems odd at first that Wenwu said the Mandarin is an Atrocious Alias, considering that in All Hail the King, he is referred to as the Mandarin by Jackson Norriss, a member of the Ten Rings, which would have only been a little over ten years ago in the timeline. However, it's most likely Killian chose a name Wenwu had used in the past as the latter is over a thousand years old and would have stopped using the name "Mandarin" a long time ago. Since the title has since decayed into being given to foods, he considers the name to be an in-universe Old Shame but still finds it amusing how it was being used.
It also ties into Killian's total tastelessness, as he clearly picked the "Mandarin" name because it sounded intimidating in his mind. This is the same guy who had no idea what King Lear was, so of course he picked a name that was completely tasteless to the rest of society.
The "Will Return" Caption at the end is a Double Meaning; it both refers to the Ten Rings as an organization, seeing Xialing updated them into a more modern age, but also to the Ten Rings themselves wielded by Shang-Chi as an indirect way of saying that he will return as well.
Shang-Chi mentions that Xialing is doing away with the Ten Rings or something to that effect in the ending. The Stinger shows that technically she is out to do that, by leading it and adding in a ton of changes to the old organization.
The Stinger mirrors Iron Man, the other film in the franchise aside from Iron Man 3, to heavily feature the Ten Rings by having a man show up and tell our hero or heroes about how they have just entered a whole different world and their lives will never be the same again because of their new roles and what they accomplished. It's even the first movie in a specific saga to take place in the present day similar to Iron Man as Black Widow (2021) was a prequel.
When we first meet Shang-Chi, he is firmly in the "Shaun" persona that he has cultivated after leaving behind the Ten Rings and while he still has reminders of his old life, he likes to forget it and focus on just his nice, carefree life. But then the Ten Rings attack him and steal his pendant, which shows that his old life has caught up with him and he spends most of the rest of the movie in Shang-Chi mode, though a part of him seems to clearly want to just go back to being "Shaun". The Stinger shows that he can to do both. Immediately after he is told by Wong that his and Katy's lives will never be the same and that he has essentially entered into the full-time job of being a superhero, he accepts that but still decides to go out late for karaoke because that is who he was as "Shaun". He has reached a blend of those two personas.
The first song that Shang-Chi and Katy sing at karaoke is a "A Whole New World" from Aladdin. This could easily serve as foreshadowing for how not only do they enter a whole new world in terms of being a superhero and having their lives changed at the end, but they both enter a whole new world in Ta Lo. For Katy specifically, everything is a whole new world as she had no idea about any of this prior to learning who "Shaun" really was while Shang-Chi has some familiarity with it.
On a related note, when Wong joins Katy and Shang-Chi during the Stinger, they sing The Eagles' "Hotel California." This is more than a Call-Back to Katy's use of it in her attempts at Confusion Fu; the lyrics point out that "You can check out anytime you want, but you can never leave." This mirrors the fact that Shang-Chi and Katy are being irrevocably sucked into the "circus" of being a superhero and companion affiliated with the Avengers, whether they want to be or not.
The new armor Shang-Chi and Xialing are given are red and white, respectively. Why? Because those are the colors of the guardian dragon. The dragon used to be red, but after sealing the Dweller-in-Darkness, it give away most of its scales to create the barrier and to the surviving humans to create weapons, leaving the dragon’s body mostly white.
Meanwhile, the Ten Rings wear black, and Shang-Chi's and Xialing's armors both have black highlights in them, showing their connection to their father's army. Plus, the Ten Rings' use of black hints at their mission being opposed to that of the Great Protector, who is white. The Great Protector's job is to contain or defeat the Dweller-In-Darkness, who has made Wenwu and, by extension, the Ten Rings, its pawn.
Xialing's Ten Rings logo is a combination of the Ta-Lo lotus (Ta-Lotus?) from her mother's home and her father's Ten Rings logo, an insignia that reflects her dual heritage.
The usage of Swae Lee and Jhene Aiko's "In the Dark" during Shang-Chi and Katy's arrival and sightseeing in Macau not only fits sound/aesthetic-wise, there's also arguably some subtexts at play:
First, while the song itself (and its music video) suggests it's about unrequited crushes, you can also argue it underlies the shared Heritage Disconnect both Shang-Chi and Katy have with the mainland Chinese sphere (both growing up more Americanized).
Second (arguably more on the Ship Tease side), it can also refer to Shang-Chi and Katy's friendship throughout the film—in that while they're arguably each other's most trusted person, the reveal of Shang-Chi's Ten Rings heritage made their differences pretty stark.
Third (and more plot-relevant), the sentiment might also be nearly the same feeling Xialing (the person they're looking for in Macau) has about her father and brother, who neglected her emotionally for years.
Why does Trevor spend a segment of the battle pretending to be dead? He's a Shakespearean actor, so it'd only be natural to channel Falstaff.
Why would someone like Bruce Banner be interested in something like the Ten Rings? Well, given how his old friend Tony Stark liked to tell him stories about his exploits, it wouldn't seem too farfetched that he would bring up his imprisonment by the Ten Rings. And finding out that the Ten Rings are an actual object that the organization named themselves after would likely encourage Bruce to learn about them on behalf of Tony.
If you take Iron Fist as canon, which the Other Wiki still does, it actually establishes a few of the rules of this film.
Dragon that acts as the protector of a small, East Asian village? Check.
Small East Asian village that is magically hidden? Check.
The power of the dragon to imbue weapons with its own magic? CHECK.
Fridge Horror
The Dweller in the Darkness ate those souls; those killed are outright completely destroyed. No afterlife. Wen Wu even in death is denied being with his wife let alone the others.
Who can say if it actually destroyed their souls? Maybe with Shang-Chi finally killing the Dweller, he freed not only the soul of his father, but of everyone else it consumed. When Nan leads the victims' memorial, she assures the survivors that the victims will rest with their ancestors, and eventually reunite with their own descendants.
The Stinger shows that the Ten Rings are sending a beacon out somewhere, and the characters have no idea who the beacon is being sent to. Let's hope that they are friendly. That said, given that in the comics, the rings belonged to Fin Fang Foom and the Makluans, they probably won't be.
Xialing in The Stinger seems a little ominous, because while she seems to be on fairly good terms with her brother at the end, her taking over the Ten Rings at the end might not be a good thing because she seems to echo her father in some ways with regards to power seeking and while the Ten Rings might seem to be more progressive they could very well lead to doing some of the same things Wenwu did, this could very well lead to a Thor and Loki type scenario where they love their sibling but are still or could be a dangerous threat.
Earlier, she'd stated that if her father won't let her inherit his empire, she'll build her own. Well, now she's inherited his, and is rebuilding it to suit her... but what's she going to do with it? Her character could go either way.
Shakespeare since the 1980s. And having a form of free entertainment by imprisoning a guy who knows his work incredibly well is just too good to pass up.