From Bananas Wiki
Pups; are the offshoots of the mother plant through the growth of the corm and root system. Suckers grow off the corm through the roots
Water suckers; smaller plant and smaller fruit bearer and a generally weaker plant. less vigor, weaker root system, less connection with the mother corm.......
Sword suckers; longer thinner with pointier leaves but a stronger root system and a better connection with the corm