I'm not entirely sure this is correct, it's just a guess:
Show - Conformation in the show ring. Bred specifically to the breed standard, so as to do well.
Gamebred - To be "gamebred" is to have the strong will to never quit a task, an essential quality in many hunting/working dogs. It is determination and courage. However, in Pit Bulls, this would be the tenacity in the fight ring.
Performance - To be "performance bred" in any breed is to be bred to have the physical and mental characteristics needed in order to perform a specific task, such as sledding, weight pulling, police work, etc.
These different "breedings" could be in any breed, not just APBT.
Again, totally a guess, based on pieces of information I've gathered throughout the years. If anyone can lend a hand, or correct this, that'd be great.
-Rosefern