shut up vs button up

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

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

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

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

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

shut up (verb)	button up (verb)
cause to be quiet or not talk	refuse to talk or stop talking; fall silent
refuse to talk or stop talking; fall silent
place in a place where something cannot be removed or someone cannot escape