calm down vs hush

calm down is not a noun while hush is a noun.

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

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

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

calm down (noun)	hush (noun)
	(poetic) tranquil silence

calm down (verb)	hush (verb)
become quiet or less intensive	become quiet or still; fall silent
make calm or still	cause to be quiet or not talk
become quiet or calm, especially after a state of agitation	run water over the ground to erode (soil), revealing the underlying strata and valuable minerals
	wash by removing particles
	become quiet or quieter