calm down vs hush up

calm down and hush up both are verbs.

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

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

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

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