shut up vs shush

shut up is an adjective but shush is not an adjective.

Word	Noun	Adjective	Verb	Adverb
shut up	No	Yes	Yes	No
shush	No	No	Yes	No

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

Other hyponyms of shut up include calm down, lull, shout down, gag, muzzle.

shut up (adjective)	shush (adjective)
closely confined

shut up (verb)	shush (verb)
cause to be quiet or not talk	silence (someone) by uttering `shush!'
refuse to talk or stop talking; fall silent
place in a place where something cannot be removed or someone cannot escape