Equine is the adjective and collective noun designating all members of the genus Equus and things pertaining to them. The genus Equus includes the domestic horse (Equus caballus), the domestic donkey (Equus asinus), the mountain zebra, plains zebra, and Grevy’s zebra, the onager, and the Przewalski’s horse — the only surviving truly wild horse species. Mules (horse dam crossed with donkey sire) and hinnies (donkey dam crossed with horse sire) are equine hybrids; they are sterile but otherwise healthy and fully capable of work.
All modern equines evolved from a single line of odd-toed ungulates originating in North America approximately 55 million years ago. The ancestral species migrated to Eurasia and Africa across land bridges before the Pleistocene and diversified into the modern species distribution. Domestic horses and donkeys were re-introduced to the Americas by European colonizers in the 15th and 16th centuries; there are no wild equines native to the modern Americas, though feral populations (mustangs, burros) have established themselves.
The term equine appears throughout veterinary, legal, and equestrian contexts. Equine veterinarian refers to a veterinarian who specializes in horses and related species. Equine law covers the legal landscape of sales, boarding, liability, and event regulation specific to horse ownership and competition. Equine herpesvirus and equine infectious anemia use the adjective to specify that the pathogen is host-specific to the Equus genus or has a primary equine presentation.
See also equine herpesvirus and equine infectious anemia, two diseases that carry the adjective because they are host-specific to this genus, and the gaits of the horse as the primary observable characteristic that distinguishes equine locomotion across the genus.
Further Reading: The evolutionary history, species list, and taxonomy of the genus are covered on Wikipedia’s Equus (genus) article.