In Superchess, there are a couple of categories:

Royal pieces (King and Emperor)
Power pieces (Amazon, Grand Duke, Maharaja, Minister)
Main pieces (Queen, Empress, Marshall)
Short distance strong pieces (Baron, General, Elephant, Veteran, Guard)
Long distance strong pieces (Counsellor, Countess, Duchess, Marquis, Princess, Siege Tower)
Light pieces (Archer, Bishop, Giraffe, Herald, Knight, Watch Tower)
Special Pieces (Angel, Ambassador, Femme Fatale, Joker, Magician, Nymph, Prince, Rook(!!))
Reserve pieces (Commando, Parachute)
Spies (Spy, Spy Catcher, Secret Agent, Infiltrator)
Crypto-spies (Clown, Dancing Girl, Dragon, Treasurer)
Pawns (normal pawn, q-pawn, t-pawn, rapid pawn, superpawn, mobilization pawn)