gag vs sick joke

gag and sick joke both are nouns.

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

As nouns, sick joke is a hyponym of gag; that is, sick joke is a word with a more specific, narrower meaning than gag:

gag (noun)	sick joke (noun)
restraint put into a person's mouth to prevent speaking or shouting	a joke in bad taste
a humorous anecdote or remark intended to provoke laughter

gag (verb)	sick joke (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