shut up vs calm down

shut up is an adjective but calm down is not an adjective.

Word	Noun	Adjective	Verb	Adverb
shut up	No	Yes	Yes	No
calm down	No	No	Yes	No

As verbs, calm down is a hyponym of shut up; that is, calm down is a word with a more specific, narrower meaning than shut up:

Other hyponyms of shut up include shush, lull, shout down, gag, muzzle.

shut up (adjective)	calm down (adjective)
closely confined

shut up (verb)	calm down (verb)
cause to be quiet or not talk	become quiet or less intensive
refuse to talk or stop talking; fall silent	make calm or still
place in a place where something cannot be removed or someone cannot escape	become quiet or calm, especially after a state of agitation