family Belonidae vs fish family

family Belonidae and fish family both are nouns.

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

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

family Belonidae: ferocious fishes of warm regions resembling but unrelated to the freshwater gars
fish family: any of various families of fish

family Belonidae (noun)	fish family (noun)
ferocious fishes of warm regions resembling but unrelated to the freshwater gars	any of various families of fish