And there's a fourth different thing (or maybe it would be a special case under Chuck's "growing a living music") -- a la Dallwitz and some others of that generation of Australians, falling in love with an older style or styles and inventing some music that's kind of in the style of but is essentially new, expressive of your own reality, and as rich in purely musical terms as, say, the best of Morton. Sounds damn unlikely, but it happened. May never happen again, not until and if we colonize other planets or galaxies (or vice versa).
Now you are talking about developments within "playing within a style". This is not too far removed from the "HIP" classical movement.
If you want to be kind, you can call it "neo-something" but it is still a sort of nostalgia thing.