ball carrier vs footballer

ball carrier and footballer both are nouns.

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

As nouns, footballer is a hypernym of ball carrier; that is, footballer is a word with a broader meaning than ball carrier:

ball carrier: (football) the player who is carrying (and trying to advance) the ball on an offensive play
footballer: an athlete who plays American football

Other hypernyms of ball carrier include football player.

ball carrier (noun)	footballer (noun)
(football) the player who is carrying (and trying to advance) the ball on an offensive play	an athlete who plays American football