Not sure what GENRE or SUB-CATEGORY your story will have to fall under? Unfamiliar or unclear about certain terms? This guide will help you by giving short explanations for the meanings of each.
Action/Adventure - this type of fiction usually focuses on fight scenes, but it also applies to stories where characters go on some sort of quest or journey. It is unlikely in fanfiction that this becomes the main genre, as it’s usually paired with romance, tragedy, and humor. Unless of course the fandom calls for it, e.g. Naruto, Dragonball, Lord of the Rings, etc.
Angst - Oh, the hurt and the pain. This story would refer to emotional wounds and internal conflicts suffered by a character. They revisit their traumas, fears, general frustrations, weeping about their miseries and woes - all in excruciating detail. But that doesn't mean, the character/s can't have a happy ending!
Alternate Universe or AU - a type of story in which characters interact in a non-canonical setting, storyline or premise. This usually involves changing certain events, characters, motives, and settings; wherein these changes must be a contradiction to canon, if not ever happening to their original universe. The thought usually of this story is “what if”s and “what might have been”s.
Crossover - Literally, "crossing over" from one fandom to another. A character/s from a fandom exists, visits, or is transported to the universe of another fandom. And then the fun begins as they blend and interact with each other.
Drama - Drama tells a serious story, deals with a lot of emotions and serious topics, which is sometimes theatrical or cliched. But drama is not driven by merely tears and conflicts, unlike angst, it shows the emotional growth of characters through their interactions and a greater understanding of their truths.
Hurt/Comfort - This style requires a character who is injured, whether physically or emotionally, as another character/s would give them comfort, either by saving them or just making them feel better again. The classic scenario in this type of fic is driving at a romantic relationship between the characters (if it doesn't exist already), but not necessary.
General - General or Gen fics are those which do not fall into any of the specific categories. This type expands a writer's creativity, as these do not carry any romantic or sexual overtones.
Horror/Supernatural - This is a rather overlooked genre in fanfiction, unless of course the fandom is of the genre itself. Basically, it involves anything gruesome or scary or creepy or completely "out of the fandom universe" world. Ghosts, vampires, a psycho-killer on the loose...
Humor/Comedy - The total opposite of drama. There is silliness, craziness, and weirdness - all for sake of a few laughs and fun.
Introspection/Character Study - This is a fairly new genre, a subcategory that falls somewhere between angst and drama. It focuses on one character but misery isn't a requisite. Sometimes it involves epiphanies or realizations. It really is just studying on how and why a character behaves as such, usually by getting into his/her head or having another character observe him/her.
Lemon/Lime - Basically a title given to a story that has explicit or implied sexual content and themes. Although the term was originally coined from an early porn anime that didn't have a plot, most fanfiction writers give a little more emotional exploration and character development when writing Lemon or Lime; and that's what distingushes it from the Smut/PWP stories.
Mystery/Suspense - Similar to Horror, and is often understated. The scary/creepy part is not a necessary requirement. Anything that deals with a baffling or enigmatic event, or arouses curiousity. It often spills into Horror, but Detective stories count as Mysteries as well.
Parody/Crack - Parody is a story that imitates or copies a particular work of another writer and giving it a satiric undertone, sometimes just for the sake of comedy. Originally termed as pastiche. Crack is a close relative of Parody, although not quite distant from Humor either. The insanity of the story can be deliberate or just simply... crazyWTFhumor.
Romance/Fluff - Ah yes, what dreams are made of: cloud nine and gushes. Romance is... romance; involves extreme liking, infatuation, passion and of course, love. Fluff is the cuter, more lighthearted and saccharine-induced type of story - the total opposite of angst.
Sci-fi/Fantasy - Sci-fi or "Science fiction" creates an alternate reality wherein the usual human changes, problems, etc are dealt with through science and technology; and might pertain to some futuristic alter-worlds. Fantasy, on the other hand, uses magic or supernatural forces as elements. The lines for these types of work are still a bit obscured, but similarities are apparent.
Smut/PWP - PWP is "Plot? What Plot?" or "Porn Without Plot" because it usually involves sexually graphic content that well, doesn't really have a plot. It's simply for the sake of writing sex scenes and pointless sexcapades.
Song/Poetry - the fic incorporates the lyrics of a song or a poem into the story and is based entirely upon it. It could also either set the mood to the story or simply as an inspiration.
Tragedy/Dark - a story that involves copious amount of mental and emotionally scarring for the character/s. Pretty much like angst, but in a broader sense such that, it goes well and beyond one character. When there's pain, depression, trauma and/or death, it usually goes under this heading.
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For more information, you can visit this webpage, where more terms of fanfiction-dom are explained:
Fanfiction Glossary of Terms