button up vs keep mum

button up and keep mum both are verbs.

Word	Noun	Adjective	Verb	Adverb
button up	No	No	Yes	No
keep mum	No	No	Yes	No

As verbs, button up and keep mum are synonyms defined as:

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

button up (verb)	keep mum (verb)
refuse to talk or stop talking; fall silent	refuse to talk or stop talking; fall silent