I agree with Tessa. A Paint is a Paint because he's painted!
Of course, a solid colored Paint is still a wonderful being with all the same qualities as a painted Paint. I just think for purposes such as showing and breeding, there should be a distinction. For example, there are classes at some shows designated for Mares, Geldings, or Studs...and at Paint shows, there are often classes designated for solid color Paints vs. painted Paints.