closer vs nigher

closer is a noun but nigher is not a noun.

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

As adverbs, closer and nigher are synonyms defined as:

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

Other synonyms of closer include nearer.

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

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