Cebidae vs mammal family

Cebidae and mammal family both are nouns.

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

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

Cebidae (noun)	mammal family (noun)
all the New World monkeys except marmosets and tamarins	a family of mammals