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.