Difference Between a Mod/Fan-Game/Hack?

[Moonface]

I was making a different thread originally but a question to Shira about it turned into a big debate that has now led to the thread being this.

So to you, what is the difference between a fan game, a ROM hack, and a game mod? I initially thought there was a clear distinction between the three but the more examples I started becoming aware of the more I kept discovering overlap, so now I don't have a clue really where the line is drawn on each of those three terms.

At best I can decide a game mod is definitely something that is modifying the vanilla game experience like changing character skins, textures, frame rate, etc. but then there's something like Super Mario Sunshine Eclipse which is the vanilla game but adds in a ton of new areas, so is that a mod or is that a ROM hack? Is Fallout London a fan game or no because it requires Fallout 4 to actually run it, despite everything about it being entirely brand new?

See where I'm starting to find this difficult now?

[ShiraNoMai]

Fan Game: Completely unique engine based on an existing IP

ROM Hack/Patch: Making new content using an existing game's engine and assets as a base. Generally entails console games, usually ROM-based ones (pre-executable launch files).

Mods: Making new content for an existing game's engine and assets as a base. Generally entails PC games with executable launch files.

[Maniakkid25]

I can push on this a little bit, because there are games that blur the line between Fan Game and ROM hack. The one that immediately comes to mind is Final Fantasy VII on the NES. No, not that one. This one. This is a hack of the Chinese NES FF7 that uses custom made sprites, maps, and all sorts of stuff to tell a version of the story that is much more accurate to the original. Is it a Fan Game? A ROM Hack? Both?! ...Yeah, it's probably both, but that's kind of my point.