shut up vs hush up

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

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

As verbs, shut up and hush up are synonyms defined as:

Other synonyms of shut up include hush, quieten, silence, still.

shut up (adjective)	hush up (adjective)
closely confined

shut up (verb)	hush up (verb)
cause to be quiet or not talk	cause to be quiet or not talk
refuse to talk or stop talking; fall silent	cover up a misdemeanor, fault, or error
place in a place where something cannot be removed or someone cannot escape