button up vs shut up

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

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

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

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

button up (adjective)	shut up (adjective)
	closely confined

button up (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