H.O.R.S.E. and H.O.S.E. are both popular mixed game variants, but they differ in the specific poker disciplines included. H.O.R.S.E. stands for Hold’em, Omaha Hi-Lo, Razz, Seven Card Stud, and Seven Card Stud Hi-Lo, while H.O.S.E. replaces the Razz component with Seven Card Stud.