hush up vs calm down

hush up and calm down both are verbs.

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

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

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

hush up (verb)	calm down (verb)
cause to be quiet or not talk	become quiet or less intensive
cover up a misdemeanor, fault, or error	make calm or still
	become quiet or calm, especially after a state of agitation