(This article has a real-world perspective)
Fan fiction is a broadly-defined term for fan created stories about characters or using the settings based off a creative universe of a commercial series/movie. As such fan fiction has no standing in terms of canon within the work it is based off.
Star Trek: The Farthest Star is a fan fiction based in the Star Trek universe. It is primarily focused on original ships and characters (as in they do not exist in canon), though it strives to be as consistent with canon as possible.