scorekeeper vs scorer

scorekeeper and scorer both are nouns.

Word	Noun	Adjective	Verb	Adverb
scorekeeper	Yes	No	No	No
scorer	Yes	No	No	No

As nouns, scorekeeper and scorer are synonyms defined as:

scorekeeper and scorer: an official who records the score during the progress of a game

scorekeeper (noun)	scorer (noun)
an official who records the score during the progress of a game	a player who makes a score in a game or contest
	a logger who marks trees to be felled
	an official who records the score during the progress of a game