dirty joke vs jest

dirty joke and jest both are nouns.

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

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

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

dirty joke (noun)	jest (noun)
an indelicate joke	activity characterized by good humor
	a humorous anecdote or remark intended to provoke laughter

dirty joke (verb)	jest (verb)
	act in a funny or teasing way
	tell a joke; speak humorously