right hander vs right-hander

right hander and right-hander both are nouns.

Word	Noun	Adjective	Verb	Adverb
right hander	Yes	No	No	No
right-hander	Yes	No	No	No

As nouns, right hander and right-hander are synonyms defined as:

right hander and right-hander: a person who uses the right hand more skillfully than the left

Other synonyms of right hander include righthander.

right hander (noun)	right-hander (noun)
a person who uses the right hand more skillfully than the left	a person who uses the right hand more skillfully than the left
	(baseball) a pitcher who throws with the right hand