right-handed pitcher vs right-hander

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

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

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

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

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