A Paint is APHA registered with strict bloodline (QH or thoroughbred) requirements, a distinct body, and must meet minimum color requirements. A Paint can be registered as a Pinto, but it is rare for a Pinto to meet Paint requirements. The Pinto Horse Association of America considers Pintos recorded in their registry as a true breed and accepts solid offspring of registered Pinto parents as breed stock, but it is a color registry.
I was able to register my horse as a Pinto to attend the Pinto world show and he's not registered anywhere else -we have no idea what his parentage is. He simply met the requirements of the amount of white on specific parts of his body, and was not obviously draft or appy. Which we think is funny, because everyone that sees him thinks he has draft in him, or appy.