fanfiction

Fanfictions are, as the name indicates, stories created by fans based on characters of TV series, movies, books, anime/manga series, etc. or even real people such as actors, famous celebrities, singers, or sportspeople. Original owners have nothing to do with them 99% of the time, and are mostly written with no economic purposes (in fact, you can be sued if you do that with characters that belong to someone else!) Fanfictions are also known as fanfics, or just fics, and are very popular on the internet.

one-shots

One-shots are a kind of fanfiction - it refers to a story that lasts only one chapter. While it doesn't allow certain things (ie. showing evolution in the characters as the time passes), it's true that one-shots can be complex and solid stories, and much easy to read than multi-chaptered fanfiction. In certain cases it's convenient to use this format; for example, when a story is impossible to be divided.