designated hitter vs batter

designated hitter and batter both are nouns.

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

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

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

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

designated hitter (noun)	batter (noun)
a ballplayer who is designated to bat in place of the pitcher	a liquid or semiliquid mixture, as of flour, eggs, and milk, used in cooking
	(baseball) a ballplayer who is batting

designated hitter (verb)	batter (verb)
	make a dent or impression in
	strike violently and repeatedly
	strike against forcefully