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Tricky question to answer.

Ultimately, I think it's how recognizable the source is in your story. Say if I took the Harry Potter world and wrote a story without any of the characters and somewhere entirely different than Hogwarts/England. However, I'm using the same magic mechanics (spell names, how they function, what resources are needed), social structure (magic users kept hidden in plain sight), creatures/monsters, and history. That would still count as a fanfiction because I'm borrowing another person's work in the fundamental rules and setting. Sort of like borrowing a stage that's been set up for another play.

It'd work the other way too. If I'm using canon characters, but in an entirely different setting that might have different world rules (like the common high school AUs), that's still fanfiction. In fact, I have one fanfic (it's on hold, unfortunately) that takes an action-platformer game and transforms it into an action-light slice-of-life story. The majority of scenes take place in a location that's nowhere in the game (because it focuses on civilian life) and the canon characters are mostly in the background. But it's still a fanfic because I'm borrowing ideas.

Where a fanfic crosses over into an original work... like I stated, I think it's when the source material is almost entirely unrecognizable in the finished work. Someone who read it without knowing it started as a fanfic might recognize similarities, but there isn't enough to recognize it as a fanfic. To go back to the Harry Potter example, if I take that idea, then retool most of the stuff I borrowed to bring it further away from the source, then it would start to be an original work even though it's at a school that teaches magic. At this point, I'd have to recognize where Rowling also borrowed ideas (most of the creatures are commonplace in mythology, the spells are adapted from another language). Those items are 'safe' to use for original work, but using too many in the same manner would be a stronger tip that it is a fanfic.

Basically comes down to the judgment of the author and the readers.

From a purely legal perspective, if you are using names and or places that are owned by a specific author, that means that an author or their estate owns the copyrights to, then what you're wiring is either fan fiction or plagiarism.

Example, the word "hobbit" is copy written and owned by the Tolkien estate. That is why all other D&D style books, RPGs, movies, etc. use the term "halfling" instead. The word "mithril" was also invented by Tolkien, however, he did not copywriter that one, and so it is now public domain and can be used by anyone.

So, if you're writing a story and you use the word "hobbit" then it BETTER be a fan fiction, dude. Otherwise you'll be slapped with a lawsuit. However, you are free to use mithril to your heart's content. So, the line between fan fiction and original work isn't so much determined by how much of another work you use, but whether or not if that other work is legally owned by someone else. You would either have to pay royalties, or else get slapped with a lawsuit.

I see, that makes sense
Thank you for the advice