buy (something) on credit
To buy something with the promise of paying for it later, as with a credit card as opposed to cash. I ran out of money at Christmastime and had to buy some presents on credit, so I'm dreading my next credit card bill.
buy something on credit
to purchase something now and pay for it later (normally plus interest). Almost everyone who buys a house buys it on credit. I didn't have any cash with me, so I used my credit card and bought a new coat on credit.