hush up vs gag

hush up is not a noun while gag is a noun.

Word	Noun	Adjective	Verb	Adverb
hush up	No	No	Yes	No
gag	Yes	No	Yes	No

As verbs, gag is a hyponym of hush up; that is, gag is a word with a more specific, narrower meaning than hush up:

Other hyponyms of hush up include shush, calm down, lull, shout down, muzzle.

hush up (noun)	gag (noun)
	restraint put into a person's mouth to prevent speaking or shouting
	a humorous anecdote or remark intended to provoke laughter

hush up (verb)	gag (verb)
cause to be quiet or not talk	struggle for breath; have insufficient oxygen intake
cover up a misdemeanor, fault, or error	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