tuna fish vs tunny

tuna fish and tunny both are nouns.

Word	Noun	Adjective	Verb	Adverb
tuna fish	Yes	No	No	No
tunny	Yes	No	No	No

As nouns, tuna fish and tunny are synonyms defined as:

tuna fish and tunny: important warm-water fatty fish of the genus Thunnus of the family Scombridae; usually served as steaks

Other synonyms of tuna fish include tuna.

tuna fish (noun)	tunny (noun)
important warm-water fatty fish of the genus Thunnus of the family Scombridae; usually served as steaks	any very large marine food and game fish of the genus Thunnus; related to mackerel; chiefly of warm waters
	important warm-water fatty fish of the genus Thunnus of the family Scombridae; usually served as steaks