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