There are 3 basic colors of horses - black, bay and chestnut. Each color has it's own shades and special effects and descriptions, but these three colors are all there really is. There are shades of black, shades of bay and lots of different shades of chestnut. Blacks have a black body and black points. Bays have a red body with black points.
Chestnuts have a red body with non-black points.
There are other genes carried from either the sire or dam that contribute to the 'extras' - grey, roan, paint, dun markings, cream, stockings, blazes, mane and tail lighting, champagne, dappling, black flecking. All of these are like icing added on top of the basic color. A bay tobiano paint horse is a bay horse that has had a contribution of white added which takes out the pigment in the color. Take the white off the horse and it is a bay. This article concentrates on breeding for dilutes, or horses that carry the cream gene.