horse doctor vs veterinarian

horse doctor and veterinarian both are nouns.

Word	Noun	Adjective	Verb	Adverb
horse doctor	Yes	No	No	No
veterinarian	Yes	No	No	No

As nouns, veterinarian is a hypernym of horse doctor; that is, veterinarian is a word with a broader meaning than horse doctor:

Other hypernyms of horse doctor include vet, veterinary, veterinary surgeon.

horse doctor (noun)	veterinarian (noun)
a veterinarian who treats horses	a doctor who practices veterinary medicine