Any% is pretty much just the default skin for Kit, NG+ is with the bonus skins you get after completing the game which you can access from the Special Features menu and the roast duck cheat code.

The skins have boosted stats compared to the default one for Kit, Once Upon a Time in China has more stamina, Fist of Legend has more adrenaline and the roasted duck has both adrenaline and stamina increased and a smaller hitbox.

For individual levels, I'll change it to start timing as soon as you gain control of Kit. The "Emu" categories were specifically for emulator runs but I'll remove them since they aren't needed and can just be put in the regular categories.