Any number of so-called 'breeds' are based solely on color and nothing more. Pintos, Palominos and Paints are a good example. Some years back, many Appaloosas were multi-registered, meaning they were registered Appaloosas AND registered 1/2, 3/4, or 7/8 Quarter Horses or Arabians. The Appaloosa registry has since tightened its requirements. Generally, any horse may be a Pinto, even a mule, so long as it has varied markings. American Painted Horses may have Quarter Horse parents, Thoroughbred parents, or registerd Painted Horse parents. Theoretically, the wild horses in Sims that resemble Painted Horses are really Pintos, since we have no way of verifying their parentage. To confuse things even more, there are registered Solid-Coat Painted Horses (offspring of two Painted Horses with varied coats). But I doubt anyone will really care about any of this.
So, to be clear, Pintos are not Painted Horses. However, wild horses and mustangs may be Painted Horses.