hush vs calm down

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

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

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

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

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

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