dirty joke vs gag

dirty joke and gag both are nouns.

Word	Noun	Adjective	Verb	Adverb
dirty joke	Yes	No	No	No
gag	Yes	No	Yes	No

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

Other hypernyms of dirty joke include jape, jest, joke, laugh.

dirty joke (noun)	gag (noun)
an indelicate joke	restraint put into a person's mouth to prevent speaking or shouting
	a humorous anecdote or remark intended to provoke laughter

dirty joke (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