be quiet vs shut up

be quiet is not an adjective while shut up is an adjective.

Word	Noun	Adjective	Verb	Adverb
be quiet	No	No	Yes	No
shut up	No	Yes	Yes	No

As verbs, be quiet and shut up are synonyms defined as:

Other synonyms of be quiet include belt up, button up, clam up, close up, dummy up, keep mum.

be quiet (adjective)	shut up (adjective)
	closely confined

be quiet (verb)	shut up (verb)
refuse to talk or stop talking; fall silent	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