He is going to college on a football 'scholarship'. [=a scholarship offered for his ability to play football]
She is attending college on a 'full scholarship'. [=a scholarship that pays fully for a student's tuition]
She got/received/won a 'scholarship' to Yale University.
(..) - Passing? - Good. - Dribbling? - Really good. Good's not going to get you a scholarship. I meant, it's great. It's great, Dad. It's great. That's my boy. Remember, it's not how big you are. It's how big you play. (..)2009 17 Again
(..) Just talked to the scout again. He's coming tonight. You play half the game I know you're capable of... ...he's prepared to offer you a full scholarship. Free ride to college and the world's your oyster, kid. Thanks, coach. MURPHY: All right, jockstraps, let's gather up. Picture time. (..)2009 17 Again