hush up vs shush

hush up and shush both are verbs.

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

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

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

hush up (verb)	shush (verb)
cause to be quiet or not talk	silence (someone) by uttering `shush!'
cover up a misdemeanor, fault, or error