Any good piece of writing should incorporate strong plot and characterization, each driving the other. If one side is severely lacking, especially for writing, then it is understandable you’d have a much narrower scope of interest.
It seems to me that fan fiction is any fiction which has never been sanctioned or authorized by the granting authority, nor ever considered canon by the authority.
Consider an early example of Star Trek TOS. After it was canceled, Paramount licensed book companies to produce TOS based new stories. My understanding is that some were based on germs of “Phase II”, but for the most part, the authors and book companies produced new stories which, at least early on, dramatically altered the TOS universe. These books were sanctioned / authorized, but were never explicitly made canon or non-canon when they were written and marketed — therefore, not fan fiction, but declared non-canon by later policy.
If the granting authority recognizes a fan work as canon, then that work is an official part of the ‘shared universe’ — would it then be considered fan fiction?