What exactly qualifies as fanfiction?

[An Enemy Spy]

Actually to be more specific, what doesn't qualify as fanfiction? I started a Pokemon story a while ago that doesn't have any established Pokemon characters, doesn't take place in the Pokemon world, and other than the concept of the creatures themselves, has little to no connection with any official Pokemon works whatsoever.
So I was looking to see what category of fanfiction this is, and for this discussion, I'll use the types shown on TV Tropes.

Alternate Universe Fic: A story that branches off from canon at some point, creating a sort of alternate timeline. Seems like almost any stroy would qualify as this, except mine doesn't branch off from canon because mine has no connection to canon.
Continuation Fic: Again, no connection to canon.
Elsewhere Fic: This is the only one that could technically apply to mine, but it implies that the story at the very least takes place in the same universe, and my story's world is completely original.
Fix Fic: No canon to fix.
Hate Fic: No established characters to hate.
High School AU: Not even close.
Original Flavor: Nope. Mine doesn't fit the tone of Pokemon at all.
Patchwork Fic: It doesn't mix the anime, comics or games together becuase again, other than the concept of Pokemon, it has no connection.
Peggy Sue: Nope.
Revenge Fic: No characters to get revenge on.
Troll Fic: I'm not even going to acknowledge that genre.

I know that TV Tropes is not the ultimate repository of all knowledge, but elswhere, it seems like every genre I can find a description for either falls into those catagories or is at least somewhat similar to them. I could not find an established genre that mine falls into.

So is there a distinction between fanfiction and fiction that takes an element from an established source and makes something completely distinct from it?

[Trazoi]

TV Tropes has a compulsion to make absolutely everything fit tropes, so take their definitions with a heaping of salt.

My personal take on fan fiction is that it contains characters, settings or another key defining element directly from the original, i.e. Pokemon fanfiction has Pokemon in Pokeballs. If all you're taking is the concept of pocket monsters, you might have a homage, a parody, a deconstruction, or a blatant rip-off - but I wouldn't call it fan fiction.

[An Enemy Spy]

Well it is the actual Pokemon. I just don't consider them to be characters in their own right since they aren't unique.

[Trazoi]

Well yeah, if you've got actual Psyducks and such in it then I would consider it fan fiction.

Edit: It's like if I wrote a short story where my author avatar get to fly around in his own personal Star Destroyer. It's still Star Wars fan fiction even if the ship is the only Star Warsy thing in it.

[Closet_Skeleton]

Edit: It's like if I wrote a short story where my author avatar get to fly around in his own personal Star Destroyer. It's still Star Wars fan fiction even if the ship is the only Star Warsy thing in it.

If you wrote an otherwise original space opera that just happened to have an exact star destroyer copy in it then that would just be a pop culture referance.

[Telonius]

The line does get blurry sometimes. If it's just an element or two, then it's not necessarily fan fiction. (Like the star destroyer example). Now, if your world contains the essential shtick of the original - your characters suddenly discover that their midichlorians are giving them the ability to lift gigantic rocks and shoot lightning - then it's probably fan fiction.

A clear delineation is whether or not you call the shtick the same thing, or at least make the attempt to disguise it. For example, the Star of the Guardians series by Margaret Weis is a "homage" (if I'm feeling charitable), not a fanfic. "Bloodswords" instead of "Lightsabers," "Platus Morianna" instead of "Obi-Wan Kenobi," etc.

Having the defining element of the original; that has the same description, characterization, name, and function as the original? That's some version of fanfic.