In AMHR...you show in the horse's age class. 1st and 2nd place horses in each class show back in the junior and senior championship classes. Junior is 2 and under, senior is 3 and over. 1st and 2nd (champion and reserve champion) show back in the Grand Champion class, and then the top two horses are named Grand and Reserve Grand Champion. At this point all classes have been divided by gender, so you have a Grand champion mare, grand champion stallion and grand champion gelding. Some shows offer supreme champion (or champion of champions)--the title varies. In that case, the three grand champion horses compete for the supreme title.
AMHR, if course, has one set of classes for Unders and another set for Overs--the two sizes do not compete against each other.