hush up vs shut up

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

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

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

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

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

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