chordate family vs family

chordate family and family both are nouns.

Word	Noun	Adjective	Verb	Adverb
chordate family	Yes	No	No	No
family	Yes	No	No	No

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

chordate family (noun)	family (noun)
any family in the phylum Chordata	primary social group; parents and children
	people descended from a common ancestor
	a social unit living together
	(biology) a taxonomic group containing one or more genera
	a collection of things sharing a common attribute
	an association of people who share common beliefs or activities
	a loose affiliation of gangsters in charge of organized criminal activities
	a person having kinship with another or others