Supernatural Fiction

Supernatural Fiction is what you call fictional stories about the supernatural. That is, it's what you call them when you're not calling them Fantasy.

While fantasy is a very broad genre, covering all manner of stories about magic, the supernatural, and the otherworldly, for most people the words "fantasy fiction" are associated first and foremost with High Fantasy: epic action/adventure stories set in an imaginary world full of flying dragons, sword-wielding heroes, fireball-slinging wizards, and all that jazz. Because of this, some stories that contain one or more elements of fantasy won't be called fantasy; they'll be called supernatural fiction, to indicate that, yes, they contain fantastical elements, but aren't what people usually think of when they hear the word "fantasy" (not-so-coincidentally, this can also help a story avoid the Sci Fi Ghetto).

Common reasons a story might be called supernatural fiction (or possibly "paranormal fiction") are:

The setting. Supernatural fiction is almost invariably set in the real world, while stories set in Constructed Worlds are pretty much always called fantasy (though plenty of stories set in the real world are called fantasy too).
The genre. While the supernatural fiction label is often applied to tales of mystery, suspense, romance, or personal drama, it's rarely applied to adventure stories; those are usually called fantasy. Meanwhile, Horror stories with supernatural elements are mostly still just called horror stories.
The point of view. Supernatural fiction is often told from the Point of View of ordinary people who aren't aware of the supernatural until they encounter it during the story. If the point of view characters have been embroiled in the supernatural since before the story began, it's more likely to be called fantasy.
The prevalence of the supernatural. In supernatural fiction, there may be only one or two supernatural elements at play, rather than whole communities of supernatural beings as is common in High and Urban Fantasy.
The form of the supernatural. Both dragons and ghosts are supernatural beings, but stories about dragons are normally called fantasy, while stories about ghosts are normally called supernatural fiction (when they're not called Horror). This may be because very few people believe that dragons are real, but there are a great many people who believe that ghosts are real. In this regard, supernatural fiction can be seen as a counterpart to supernatural non-fiction. There are many non-fiction books containing supposedly true accounts of haunted houses, demonic possessions, and occult rituals, and supernatural fiction often draws inspiration from these stories, portraying their supernatural content in a way that emulates the tone, if not the details, of what real people have claimed to have experienced. (If the author claims the supernatural elements of their story actually exist, then you've entered the murky territory separating Supernatural Fiction from religious fiction.) Meanwhile, if a story is called fantasy, it's more likely to craft its supernatural elements from pure imagination, with only a token resemblance to real life supernatural beliefs. Generally speaking, a witch giving someone boils by calling on pagan gods and performing an arcane ritual is likely to be supernatural fiction; a witch turning someone into a mouse by wiggling their nose is likely to be fantasy.

See also Gothic Horror, which Supernatural Fiction is often inspired by, Paranormal Romance, a popular Sub-Genre, and Magical Realism, another kind of fantasy-that's-not-called-fantasy.