cover up vs hush up

cover up and hush up both are verbs.

Word	Noun	Adjective	Verb	Adverb
cover up	No	No	Yes	No
hush up	No	No	Yes	No

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

Other hyponyms of cover up include gloss over, sleek over, whitewash.

cover up (verb)	hush up (verb)
hide from view or knowledge	cause to be quiet or not talk
	cover up a misdemeanor, fault, or error