Genetically a 'True Black' or 'Jet Black' horse is either homozygous dominant (EE), or heterozygous (Ee), because only one copy of the dominant allele is necessary for the black color to be expressed. If the horse was genetically a chestnut then it would be homozygous recessive (ee).
Where as a 'Bay' horse has the agouti gene which restricts black to the points (the nose, ears, mane, tail, and knee/hock down on all four legs). So a bay horse (or a buckskin, or dun) would carry the genes either as homozygous dominant (AA) or heterozygous (Aa), where a black horse would not have this gene and be heterozygous recessive (aa).
So really genetics are what define a horses color for me because there really isn't always a cut and dry option, because with all the modifer genes a horse can quickly start to look like it might possibly be another color. I've even see some people register their horse a certain color that isn't even genetcally possible because their parents don't even carry the right genes but they "look" like that color.
Does any of that make sense?? What colors were the sire and dam??