Debit cards (called "check cards" here) are becoming more popular lately. Thanks to the aggressive adoption of credit cards, the infrastructure to handle debit cards was already there by the time the government decided to extend the tax credit to debit cards as well. Nowadays it's a toss-up between credit cards and debit cards.
But what we call credit cards here is a bit different from the American counterparts. Most Korean credit cards require you to pay the whole balance every month, unless you specifically request a different payment plan at the time of purchase. The amount you have to pay for each of the next few months, including interest, is also fixed at the time of purchase. You can't just pay an arbitrary fraction of your balance or transfer your balance to another card. So it's halfway between a traditional charge card and an American-style revolving credit card. Some banks do have revolving credit cards available, but AFAIK they are not very popular.