shush vs hush up

shush and hush up both are verbs.

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

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

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

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