funny story vs gag

funny story and gag both are nouns.

Word	Noun	Adjective	Verb	Adverb
funny story	Yes	No	No	No
gag	Yes	No	Yes	No

As nouns, gag is a hypernym of funny story; that is, gag is a word with a broader meaning than funny story:

Other hypernyms of funny story include jape, jest, joke, laugh.

funny story (noun)	gag (noun)
an account of an amusing incident (usually with a punch line)	restraint put into a person's mouth to prevent speaking or shouting
	a humorous anecdote or remark intended to provoke laughter

funny story (verb)	gag (verb)
	struggle for breath; have insufficient oxygen intake
	make an unsuccessful effort to vomit; strain to vomit
	cause to retch or choke
	make jokes or quips
	be too tight; rub or press
	tie a gag around someone's mouth in order to silence them
	prevent from speaking out