southpaw vs left hander

southpaw and left hander both are nouns.

Word	Noun	Adjective	Verb	Adverb
southpaw	Yes	No	No	No
left hander	Yes	No	No	No

As nouns, southpaw and left hander are synonyms defined as:

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

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

southpaw (noun)	left hander (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