family Equidae vs mammal family

family Equidae and mammal family both are nouns.

Word	Noun	Adjective	Verb	Adverb
family Equidae	Yes	No	No	No
mammal family	Yes	No	No	No

As nouns, mammal family is a hypernym of family Equidae; that is, mammal family is a word with a broader meaning than family Equidae:

family Equidae (noun)	mammal family (noun)
horses, asses, zebras, extinct animals	a family of mammals