is a specific kind of: Equus caballus, horse.

is a broader term that covers: remount | palfrey | warhorse | prancer | hack | cow pony | quarter horse | Morgan | Plantation walking horse, Tennessee walker, Tennessee walking horse, Walking horse | American saddle horse | Appaloosa | Arab, Arabian | Lipizzan, Lippizan, Lippizaner | buckskin | crow-bait, crowbait | dun | gray, grey ... show more.

derivation: bestride, climb on, get on, hop on, jump on, mount, mount up.