shut up vs quieten

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

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

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

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

shut up (adjective)	quieten (adjective)
closely confined

shut up (verb)	quieten (verb)
cause to be quiet or not talk	cause to be quiet or not talk
refuse to talk or stop talking; fall silent	make calm or still
place in a place where something cannot be removed or someone cannot escape	become quiet or quieter