And there's also 'fanfiction' that is completely original, either by virtue of being so transformative that only the character names remain, or even what is called 'original fanfiction', which is to say, it's produced by someone within the community, for fun, using the conventions of the community, and they give it away for free. It doesn't have any distinguishing marks that an outsider would recognize as fanfic, although it may share some style-markers.

But if the author wants to call it and treat it like fanfic, then who am I to tell them they can't call it that?