"Debit or credit?" (Debit card, which pulls the money directly from your bank account, or credit card). We hear this in the US with almost every transaction nowadays.

i never been in UK. or U.S but let me give you idea about your question most of the groceries in U.S are using paper bag cause it was biodegradable and cheaper not like pastic its non biodegradable and high cost. we are now 21st century. our society has called "cashless society" which mean people are not carry huge amount of cash in their pocket since credit card has invented. thats why most of the big super market or malls and other bussines stablishment will ask you or you can see signage in mode payments 'cash or card" cowboy...

In Australia we don't have the variety of choice, for plastic or paper bags in the one shop - most bags are plastic, though we're aiming to phase this out. Shops will have one or the other, rarely both. So we assume the question is about money, and "pay with plastic" means credit card. We ignore the fact that Australian dollars are washable polymer notes anyway. In the UK they use the term "drinking on plastic" which means you take no cash to the pub, and either use the credit card each time you buy drinks, or have it kept behind the bar for your tab. This is just adding onto Marks answer above. (Cheers mate) ;)

In oz.. If you are refering to (1) and (2) as the same method of payment, we usually hear "card or cash". e.g.. "Are you paying with card or cash?" or similar. If the customer isn't prompted with this question, then sometimes we say.. "Do you have EFTPOS?" if we want to pay by debit card, or if we want to pay by credit card, we generally say.. "Do you take x?" x = Visa, AMEX, etc.

Are you implying that "plastic or paper" and "credit card or cash" refer to the same thing? If so, this is not correct. These two phrases carry completely different meanings. "Plastic or paper" is commonly used when grocery shopping in the U.S. It refers to the material used to carry your purchases. "Credit card or cash" (also commonly used in the U.S.) refers to the form of payment. Yes, a credit card is made of "plastic" and cash is made of "paper," but the phrase "plastic or paper" has never referred to a form of payment in the U.S. Good question! :)