silence vs calm down

silence is a noun but calm down is not a noun.

Word	Noun	Adjective	Verb	Adverb
silence	Yes	No	Yes	No
calm down	No	No	Yes	No

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

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

silence (noun)	calm down (noun)
the absence of sound
a refusal to speak when expected
the trait of keeping things secret
the state of being silent (as when no one is speaking)

silence (verb)	calm down (verb)
cause to be quiet or not talk	become quiet or less intensive
keep from expression, for example by threats or pressure	make calm or still
	become quiet or calm, especially after a state of agitation