designated hitter vs slugger

designated hitter and slugger both are nouns.

Word	Noun	Adjective	Verb	Adverb
designated hitter	Yes	No	No	No
slugger	Yes	No	No	No

As nouns, slugger is a hypernym of designated hitter; that is, slugger is a word with a broader meaning than designated hitter:

designated hitter: a ballplayer who is designated to bat in place of the pitcher
slugger: (baseball) a ballplayer who is batting

Other hypernyms of designated hitter include batsman, batter, hitter.

designated hitter (noun)	slugger (noun)
a ballplayer who is designated to bat in place of the pitcher	(baseball) a ballplayer who is batting
	a boxer noted for an ability to deliver hard punches