flag officer vs admiral

flag officer and admiral both are nouns.

Word	Noun	Adjective	Verb	Adverb
flag officer	Yes	No	No	No
admiral	Yes	No	No	No

As nouns, admiral is a hyponym of flag officer; that is, admiral is a word with a more specific, narrower meaning than flag officer:

flag officer: a senior naval officer above the rank of captain
admiral: the supreme commander of a fleet; ranks above a vice admiral and below a fleet admiral

Other hyponyms of flag officer include full admiral, five-star admiral, fleet admiral, rear admiral, vice admiral.

flag officer (noun)	admiral (noun)
a senior naval officer above the rank of captain	any of several brightly colored butterflies
	the supreme commander of a fleet; ranks above a vice admiral and below a fleet admiral