I currently have four cats. All but one are rescues.
One is completely docile and will not show any aggression toward people under any provocation.
The daughter of this one was handled from the first day of life. She will make playful bites, mostly when you stop petting her. She has never hurt anyone.
A third cat will play rough, but keeps his claws tucked in. He doesn't hurt anyone.
The fourth is the devil himself. He went through four owners before landing on our doorstep. After three years he is almost safe, most of the time.
What made the most difference in his training was the appearance of the third cat, as a kittem. The dangerous one had simply never learned to play. After a few months of playing with another cat, he learned not to bite and scratch hard enough to hurt.
Either that, or the third cat made him an offer he couldn't refuse. Never underestimate the power of the Godfather cat! :-)