herring vs food fish

herring and food fish both are nouns.

Word	Noun	Adjective	Verb	Adverb
herring	Yes	No	No	No
food fish	Yes	No	No	No

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

herring: commercially important food fish of northern waters of both Atlantic and Pacific
food fish: any fish used for food by human beings

Other hypernyms of herring include clupeid, clupeid fish.

herring (noun)	food fish (noun)
commercially important food fish of northern waters of both Atlantic and Pacific	any fish used for food by human beings
valuable flesh of fatty fish from shallow waters of northern Atlantic or Pacific; usually salted or pickled