Fanfiction is like your version of telling how a popular turns out. Sort of like how Sora never really turned back from being a Heartless, but the viewers' intake of how the story goes or should be. A crossover is like Inuyasha and Kingdom Hearts both in the same story or multiple other stories within the popular plot. One thing, a fanfiction writer has to be wary of is publication rights. Because, you're writing about someone's else work, that's way it is imperative to give credit to the actual writer as to avoid plaguarism.