right hander vs righthander

right hander and righthander both are nouns.

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

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

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

Other synonyms of right hander include right-hander.

right hander (noun)	righthander (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