ball carrier vs rusher

ball carrier and rusher both are nouns.

Word	Noun	Adjective	Verb	Adverb
ball carrier	Yes	No	No	No
rusher	Yes	No	No	No

As nouns, rusher is a hyponym of ball carrier; that is, rusher is a word with a more specific, narrower meaning than ball carrier:

ball carrier: (football) the player who is carrying (and trying to advance) the ball on an offensive play
rusher: (football) a ball carrier who tries to gain ground by running with the ball

Other hyponyms of ball carrier include forward passer, passer.

ball carrier (noun)	rusher (noun)
(football) the player who is carrying (and trying to advance) the ball on an offensive play	a person who rushes; someone in a hurry; someone who acts precipitously
	someone who migrates as part of a rush to a new gold field or a new territory
	(football) a ball carrier who tries to gain ground by running with the ball