snapper vs saltwater fish

snapper and saltwater fish both are nouns.

Word	Noun	Adjective	Verb	Adverb
snapper	Yes	No	No	No
saltwater fish	Yes	No	No	No

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

snapper (noun)	saltwater fish (noun)
large-headed turtle with powerful hooked jaws found in or near water; prone to bite	flesh of fish from the sea used as food
any of several large sharp-toothed marine food and sport fishes of the family Lutjanidae of mainly tropical coastal waters
Australian food fish having a pinkish body with blue spots
a party favor consisting of a paper roll (usually containing candy or a small favor) that pops when pulled at both ends
flesh of any of various important food fishes of warm seas
(football) the person who plays center on the line of scrimmage and snaps the ball to the quarterback