Agouti is what causes bay and brown. The only two "true" horse colors are black and chestnut - every single horse in the world is either black or chestnut. The rest of the colors are just modifiers and extra genes acting on "top" of one of the two base colors.
Bay is what happens when a black horse gets agouti. Hence why two black horses can never sire a bay - if they were carrying the agouti gene to pass on, they would be bay themselves.
Sorry to hijack the thread here, but I am trying to learn more about colours. Genetically speaking what would it be with a horse who is pitch black all year round, except for being tan coloured around the eyes and muzzle?
You may be referring to "mealy". It is a modifier that causes a paler shade on the muzzle, sometimes around the eyes and often in the flank or belly area. An example of a mealy horse and a non-mealy horse:
I have two horses that are black according to the AQHA. My gelding is black. He does not 'fade' in the sun. He bleaches in his tack area from /sweat salt. He is NOT brown in the winter. My mare is a smokey black - she can bleach out all over. I do not consider her to be a true black but AQHA does not have the smokey option as a color choice.