The prevelance of this trope
The Bad Webcomics Wiki has an article here
on why the usage of Funny Animals became so popular in comics and cartoons. Some examples they discussed are Tom and Jerry and Maus utilizing Animal Jingoism and Animal Stereotypes to quickly establish character relationships and personalities, and SpongeBob SquarePants taking advantage of the unique anatomy of various animals to create an Astonishingly Appropriate Appearance that fits a character's personality.
Funny Animal or Beast Man?
Funny Animal is an animal with human traits while Beast Man is a humanoid with animal traits, but there can be a bit of confusion based solely on that distinction. Luckily, there are a few methods to more easily tell which trope this should fall under. So this analysis doesn't become full of "insert species name here", we'll use a cat as the example character we need to pick apart.First is the term. "Anthro[pomorphic] cat" or "cat - man/woman/folk/person?" English uses prepositional adjectives meaning the adjectives come before the noun, and thus we can use this quirk as a guideline to figure out whether people subconsciously think it's more a cat (Funny Animal) or more a person (Beast Man).
Second, naming. Are they called cats or are they called something else? Don't get confused with Call a Rabbit a "Smeerp" though; this has nothing to do with having two names for the same species, this is to do with having two names for two different species, à la panthera tigris (tiger) and panthera onca (jaguar). Is the cat(?) fine with being called a cat or does s/he get offended? Does s/he insist you call them by their proper species name? If the former, they're likely Funny Animal since they admit to being a cat. If it's the latter, they're likely Beast Man, since you've basically commited Son of an Ape to him/her. However, keep in mind the cat could just not comment out of politeness, so don't assume no Insistent Terminology automatically equals Funny Animal.
Third, the origins of the character. Is the cat(?) is specifically mentioned to be from space? If so, it's a dead giveaway they're a Beast Man, doubly so if the work is set A Long Time Ago, in a Galaxy Far, Far Away... where Earth is an Insignificant Little Blue Planet or even unheard of. But if they originated here on Earth, whether through genetic engineering, evolution, or a parallel universe, they should fall under Funny Animal. Note the word should - the cat might have originated on Earth, but if they're considered a distinct species they still go under Beast Man. (If you're confused how that happens, remember that birds evolved from dinosaurs and thus you can technically say they're the same animal, but you probably consider them to be two different ones.)
Fourth, the cat(?) and other cats. Furry Confusion is a dead giveaway it's Funny Animal. This is because the anthropomorphic cat character is, in the end, an animal, so confusion aside you can have an anthropomorphic and non-anthropomorphic cat, but the Cat-Person would again tell you that they're not at all related to the cat. Furry Confusion with a Beast Man would be like seeing a homo sapiens (human) with a homo erectus (the species that eventually evolved into humans), but works tend to eschew having this.
Fifth, humans. Is it a World of Funny Animals where humans don't exist? As the name implies, you're looking at Funny Animal. If humans do exist, then see what happens if you replace the animals with humans. Since Funny Animal characters are usually just substitutes for humans, the plot and premise should be barely affected, some animal-specific jokes notwithstanding. In works with Beast Man characters replacing the animals tend to throw a wrench in the whole work, since Beast Men are usually stand-ins for non-humans (similar to Rubber-Forehead Alien) and obviously you can't have a work featuring a non-human race if the characters aren't non-human.
Sixth, their actions. An anthropomorphic cat would have Furry Reminders, while a cat-person would not - the Furry Reminder is there so you remember that yes, they are a cat, but a cat-person would not as aside from appearance, they really are not that feline. Remember, a Beast Man is like a Rubber-Forehead Alien except instead of rubber it's fur.
