pitcher vs right-hander

pitcher and right-hander both are nouns.

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

As nouns, right-hander is a hyponym of pitcher; that is, right-hander is a word with a more specific, narrower meaning than pitcher:

pitcher (noun)	right-hander (noun)
the position on a baseball team of the player who throws the ball for a batter to try to hit	a person who uses the right hand more skillfully than the left
an open vessel with a handle and a spout for pouring	(baseball) a pitcher who throws with the right hand
(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