sick joke vs jest

sick joke and jest both are nouns.

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

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

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

sick joke (noun)	jest (noun)
a joke in bad taste	activity characterized by good humor
	a humorous anecdote or remark intended to provoke laughter

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