shush vs shut up

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

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

As verbs, shut up is a hypernym of shush; that is, shut up is a word with a broader meaning than shush:

Other hypernyms of shush include hush, hush up, quieten, silence, still.

shush (adjective)	shut up (adjective)
	closely confined

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