Paints are restricted to the QH and Thoroughbred breeds (both breeds are found in paints). Pintos are of any breed, so long as they have enough white (usually white above the knee, on the body, past the eye, etc). Pintos can be registered as pinto, but it is a color based registry (like the palomino registry). So a horse can be registered as a purebred of any breed, and could be double registered as pinto if it has sufficient white. So a "crop out" (solid parents, loud colored foal) purebred quarter horse would be able to be registered with AQHA, APHA and PtHA. Posted via Mobile Device
Crop out AQHA horses cannot be registered with the APHA any longer. Since AQHA lifted the white rule the are registered with the AQHA and have their papers marked "undesirable white." All APHA horses HAVE to have one APHA parent. The other can be either AQHA or JC, but one HAS to be APHA registered.
Paint is a stock breed. It started with undesirable white (crop out) quarter horses primarily. It's a semi-closed registry (like the AQHA is, as opposed to a closed registry like the AHA or an open registry like the Palomino and Pinto registries). You can add some outside breeds (TB and QH) but not very many. Sometimes you get no white markings on the foals (those are "breeding stock" or solid colored). The Breeding Stock foals would not be eligible for pinto registration, but any "normal" colored Paint would be.