hush vs shut up

hush is a noun but shut up is not a noun.

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

As verbs, hush and shut up are synonyms defined as:

Other synonyms of hush include hush up, quieten, silence, still.

hush (noun)	shut up (noun)
(poetic) tranquil silence

hush (adjective)	shut up (adjective)
	closely confined

hush (verb)	shut up (verb)
become quiet or still; fall silent	cause to be quiet or not talk
cause to be quiet or not talk	refuse to talk or stop talking; fall silent
run water over the ground to erode (soil), revealing the underlying strata and valuable minerals	place in a place where something cannot be removed or someone cannot escape
wash by removing particles
become quiet or quieter