hush vs quiet down

hush is a noun but quiet down is not a noun.

Word	Noun	Adjective	Verb	Adverb
hush	Yes	No	Yes	No
quiet down	No	No	Yes	No

As verbs, hush and quiet down are synonyms defined as:

Other synonyms of hush include pipe down, quiesce, quiet, quieten.

hush (noun)	quiet down (noun)
(poetic) tranquil silence

hush (verb)	quiet down (verb)
become quiet or still; fall silent	become quiet or quieter
cause to be quiet or not talk
run water over the ground to erode (soil), revealing the underlying strata and valuable minerals
wash by removing particles
become quiet or quieter