Does the term "Equine", only refer to the domesticated horse?

I thought equine was a group that included zebras, donkeys and mules. However, an old vet told me that this is an incorrect usage and term “equine” only refer to the domesticated horse. Is he right?

I believe “equine” only refers to domesticated (or ones descended from domesticated that are now feral) horses. Equid on the other hand refers to zebras, onagers etc.

That’s what I’ve heard at least.

FWIW reference.com has

“Of, relating to, or characteristic of a horse.”
“Of or belonging to the family Equidae, which includes the horses, asses, and zebras.”

The source they cite is The American Heritage Dictionary of the English Language, Fourth Edition

Equine can be an adjective, but equid is always a noun. When used as a noun, I’ve heard both refer to any member of the horse family (Equidae).

Equidae is a family of perissodactyls with numerous extinct genera, for example Hyracotherium (“Eohippus”), Merychippus (Paleoperissodactylologists wish each other a Merychippus and a Happy New Year each December), Hipparion, etc.

The only living genus of Equidae is Equus. It includes the horse, E. caballus, two species of ass, E. asinus and E. hemionus, and three species of zebra. “Equine” in a scientific context may mean, and “equid” always does mean, any animal in genus Equus, and likely any species of Family Equidae.

However, in a popular or applied-arts sense such as a veterinarian or animal husbandry expert might use, the term does not derive from the taxonomic clssification, but from the Classic Latin equus, i.e., the horse. (Note that everything from Clydesdales and Shire horses to Arabians and thoroughbreds to Shetland ponies is in the same species; like dogs, specialized breeds have been, well, bred.)