Pintos (not paints) are a pattern NOT a colour. You can have a paint horse with pinto patterns, or a paint horse with solid colouring. Pintos can be of any breeding.
We longer refer to them as piebald or skewbald as there are SO many different colours now they are just referred to as their base colour and white e.g. Grey/white, bay/white, chestnut/white, black/white, dun/white.
I'll link you to the NZ Pinto society where they explain the patters - depending on how your horse is marked, depends on the pattern. Obviously genetics comes into it as well but basically there are 3 main patterns - Tobiano (most common), Overo & Tovero which is a combination of the two.
Hopefully this link works :) New Zealand Pinto Society