quieten vs shut up

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

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

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

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

quieten (adjective)	shut up (adjective)
	closely confined

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