Hate to point out to you but there is only TWO base colors in horses.
Red and black. Everything else is a modification.
There are not two separate genes found at this time to cause the different shades of red in chestnut/sorrel horse. They are exactly the same genetically.
There are not two types of black (fading/nonfading). They are exactly the same genetically.
There are only three agouti (bay type) genes, bay (A), brown (At), and wild bay (A+).
Your pinto/paint genes are incorrect as well.
Pinto genes -
Maybe I should have been more clear....the BAY gene is a red BASE with black points, the variations of that gene could be anywhere from a "mahogony to a light shade of red with BLACK POINTS, ears, lower legs, mane and tail, of course there are variations of that also...with the black being just below the knee/pastern up to the mid-gaskin. Of course there are Black Bays that appear black but are BAY BASED.
There are 2 distinct variations of chestnut/sorrel...the genes have not been discovered on the allele but the work of Dr. Ann Bowling at UC Davis, California has identified a distinct variation of the red based horses (chestnut/sorrel) geneticists/testing labs for this reason do not identify the 2 distinct variations.
There is still work being done on the reason why there is a "Jet Black and a Fading Black" and which individual genes produce the variations, as stated above just because they havent identified those genes doesnt mean they don't exist. As such a testing lab won't identify the difference, although they have found that a "Jet Black" will produce more homozygousity that a "Fading Black".
They have identified a "Seal Brown" as a genetic modification on a black based animal...somewhere they believe that a bay and black had some sort of genetic miscommunication during genetic recombination. "Seal Brown" is a heterozygous trait.
Pinto/Paint variations are:
Overo...a splashed white and frame are variations of this gene.
Tobiano is a seperate mutation and can breed true or homozygous
Tovero or "medicine hat" a horse that phenotypically
will express both an overo and tobiano gene.
A "Dominant White" is an extreme variation of the sabino gene, which is thought to be a mutation of the overo gene. Since a horse can phenotypically express a sabino characteristic or an overo characteristic they are working to try and distinguish where the mutation occured. They are doing pedigree research in conjunction with the American Paint Horse Association on this. There is a beautiful TB Stallion that is a "White" which is double registered through the APHA, he is genetically an extreme sabino, his mother has produced 3 of them. There have only been 17 documented cases of "white" horses being registered through the Jockey Club.
There are also a lot of "splashed white overo" horses that are maximum whites also. A big difference between a "maximum sabino white" and a "maximum splashed white" is along the pedigree lines there are "deaf" horses being produced by the "splashed white" lines. In my opinion it has more to do with the success of those individual horses being bred than anything else.
Some very good sites to do research:
UC Davis, California
University of Kentucky
The Journal of Veterinary Medicine (usually your local library has a copy or ask your vet for his/hers)
The Animal Gentics labs are good resources but because they usually only give information on the tests they produce much more digging is required for accurate information.
If you have access to a University library, you can find current journal abstracts through there.
Brazil and Japan have been doing a lot of research but the info is difficult to get a hold of.