right-hander vs right-handed pitcher

right-hander and right-handed pitcher both are nouns.

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

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

right-hander and right-handed pitcher: (baseball) a pitcher who throws with the right hand

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