left-hander vs left-handed pitcher

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

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

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

left-hander and left-handed pitcher: a baseball pitcher who throws the ball with the left hand

Other synonyms of left-hander include left hander, lefthander, lefty, southpaw.

left-hander (noun)	left-handed pitcher (noun)
a person who uses the left hand with greater skill than the right	a baseball pitcher who throws the ball with the left hand
a baseball pitcher who throws the ball with the left hand