right-hander vs pitcher

right-hander and pitcher both are nouns.

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

As nouns, pitcher is a hypernym of right-hander; that is, pitcher is a word with a broader meaning than right-hander:

Other hypernyms of right-hander include hurler, twirler.

right-hander (noun)	pitcher (noun)
a person who uses the right hand more skillfully than the left	the position on a baseball team of the player who throws the ball for a batter to try to hit
(baseball) a pitcher who throws with the right hand	an open vessel with a handle and a spout for pouring
	(baseball) the person who does the pitching
	(botany) a leaf that is modified in such a way as to resemble a pitcher or ewer
	the quantity contained in a pitcher