Well, if they're called credits, it stands to reason that they aren't physical currency. We already use a credit-based system, one that generally relies on plastic cards -- cards that contain identification allowing vendors to connect to our financial institutions in order to record the credit-based transactions. Of course, the credit needs to be backed up with money, but that money is increasingly a purely electronic entity -- rather than sending cash to the bank that issues my credit card, I write them a check, which is permission to transfer funds from my other bank -- a transaction that's probably purely electronic. With a debit card, you can combine those two operations into a single electronic transaction. These days, there's increasingly little need for money to exist in any physical form at all.
Perhaps people in the 23rd century use a similar system but one that's more streamlined, like the debit card process. They have accounts in the UFP computer system, into which their employers deposit "credits" that they can then draw on to purchase things. And perhaps they identify themselves biometrically instead of with magnetic strips on plastic cards, thus making it an even more intangible system. Hence Kirk's inability to adapt to the use of paper money and credit cards in a 1986 pizzeria.
Perhaps people in the 23rd century use a similar system but one that's more streamlined, like the debit card process. They have accounts in the UFP computer system, into which their employers deposit "credits" that they can then draw on to purchase things. And perhaps they identify themselves biometrically instead of with magnetic strips on plastic cards, thus making it an even more intangible system. Hence Kirk's inability to adapt to the use of paper money and credit cards in a 1986 pizzeria.
