stop up vs stopper

stop up is not a noun while stopper is a noun.

Word	Noun	Adjective	Verb	Adverb
stop up	No	No	Yes	No
stopper	Yes	No	Yes	No

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

Other hyponyms of stop up include stopple, tampon, chink, cork, cork up.

stop up (noun)	stopper (noun)
	blockage consisting of an object designed to fill a hole tightly
	(bridge) a playing card with a value sufficiently high to insure taking a trick in a particular suit
	an act so striking or impressive that the show must be delayed until the audience quiets down
	a remark to which there is no polite conversational reply

stop up (verb)	stopper (verb)
fill or close tightly with or as if with a plug	close or secure with or as if with a stopper