family Rajidae vs fish family

family Rajidae and fish family both are nouns.

Word	Noun	Adjective	Verb	Adverb
family Rajidae	Yes	No	No	No
fish family	Yes	No	No	No

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

family Rajidae (noun)	fish family (noun)
bottom-dwelling tropical rays: skates	any of various families of fish