In French, I'm used to "fantastique" being used for the type of fantasy that takes place in our world/universe, especially when it doesn't affect everyone's life (Harry Potter would be an example. Lovecraft would probably qualify too) and "fantasy" for the type of fantasy that takes place in another wolrd/universe with no indication that ours exists (Tolkien falls into that category). I wasn't aware of a similar distinction in English but I guess "Urban fantasy" (with your definition) probably matches what I call "fantastique" (which really is just the old French word for "fantasy", before we adopted the English one).