nearer vs closer

nearer is not a noun while closer is a noun.

Word	Noun	Adjective	Verb	Adverb
nearer	No	No	No	Yes
closer	Yes	No	No	Yes

As adverbs, nearer and closer are synonyms defined as:

nearer and closer: (comparative of `near' or `close') within a shorter distance

Other synonyms of nearer include nigher.

nearer (noun)	closer (noun)
	(baseball) a relief pitcher who can protect a lead in the last inning or two of the game
	a person who closes something

nearer (adverb)	closer (adverb)
(comparative of `near' or `close') within a shorter distance	(comparative of `near' or `close') within a shorter distance