The difference is relatively simple.
DMC_Stylish_2_1_Specialanims: This version adapts the animations of idles and movements only for player.
DMC_Stylish_2_1: This version adapts all animations for all characters.
Use the latter if you want the animations for all characters in game, the former if you want them ONLY for your character.
Personally I use Specialanims. For one thing it makes your character seem more special as he/she has different moves.