home run vs base hit

home run and base hit both are nouns.

Word	Noun	Adjective	Verb	Adverb
home run	Yes	No	No	No
base hit	Yes	No	No	No

As nouns, base hit is a hypernym of home run; that is, base hit is a word with a broader meaning than home run:

home run: a base hit on which the batter scores a run
base hit: (baseball) the successful act of striking a baseball in such a way that the batter reaches base safely

Other hypernyms of home run include safety.

home run (noun)	base hit (noun)
a base hit on which the batter scores a run	(baseball) the successful act of striking a baseball in such a way that the batter reaches base safely
something that exactly succeeds in achieving its goal