Paint is an actual breed. To be registered in the paint horse association the horse must have parented registered in the APHA, AQHA or the jockey club. Paints do not always have patterned coat. Pinto is coloring although there has been an association started for them.
Paint is a breed. They are usually white with brown, palomino, black, chestnut, etc blotches all over. Some paints have blue eyes. But paints can also be solid colored. The color referring to being white with blotches all over is pinto. Pinto can be lots of breeds including Miniature horses, Shetland Ponies, and I believe Welsh ponies.