come down vs rain

come down is not a noun while rain is a noun.

Word	Noun	Adjective	Verb	Adverb
come down	No	No	Yes	No
rain	Yes	No	Yes	No

As verbs, rain is a hyponym of come down; that is, rain is a word with a more specific, narrower meaning than come down:

Other hyponyms of come down include rain down, spat, snow, hail, sleet.

come down (noun)	rain (noun)
	anything happening rapidly or in quick successive
	water falling in drops from vapor condensed in the atmosphere
	drops of fresh water that fall as precipitation from clouds

come down (verb)	rain (verb)
get sick	precipitate as rain
be the essential element
criticize or reprimand harshly
move downward and lower, but not necessarily all the way
fall from clouds