shut up vs suppress

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

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

As verbs, suppress is a hypernym of shut up; that is, suppress is a word with a broader meaning than shut up:

Other hypernyms of shut up include conquer, stamp down, subdue.

shut up (adjective)	suppress (adjective)
closely confined

shut up (verb)	suppress (verb)
cause to be quiet or not talk	bring under control by force or authority
refuse to talk or stop talking; fall silent	lessen to the point of stopping
place in a place where something cannot be removed or someone cannot escape	put out of one's consciousness
	consciously restrain from showing; of emotions, desires, impulses, or behavior
	come down on or keep down by unjust use of one's authority