calm down vs shut up

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

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

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

Other hypernyms of calm down include hush, hush up, quieten, silence, still.

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

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