keep quiet vs shut one's mouth

keep quiet and shut one's mouth both are verbs.

Word	Noun	Adjective	Verb	Adverb
keep quiet	No	No	Yes	No
shut one's mouth	No	No	Yes	No

As verbs, keep quiet and shut one's mouth are synonyms defined as:

keep quiet and shut one's mouth: refrain from divulging sensitive information; keep quiet about confidential information

Other synonyms of keep quiet include keep one's mouth shut.

keep quiet (verb)	shut one's mouth (verb)
refrain from divulging sensitive information; keep quiet about confidential information	refrain from divulging sensitive information; keep quiet about confidential information