Yes- pinto includes all white patterning (tobiano, sabino, splash, dominant white, and frame) except for appaloosa. Any horse who displays one of these patterns, regardless of whether or not it is registered with any registry (or no registry), is a pinto.
There is a pinto registry, but it is a color registry, not a breed. They accept most horses with any type of pinto coloring (including Paint horses). IIRC they don't accept drafts but have no other real requirements.
APHA registered horses are considered Paint horses whether or not they have inherited or display a white pattern. The registry prefers more loudly expressed pinto coloration, but allows horses who don't display it to be registered as "Solid Paint Bred" and to be used as breeding stock.