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It's stored by your bank but your credit card or account id is never transferred to the retailer by the payment processors instead what happens is that McDonalds get an unique transaction ID that only your card provider knows was generated by your card.

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So how do they know it was me who sent the money and not some McDonalds money launderer ?

McDonald's don't your bank does know you authorized an transaction using pin/card/app.

The payment terminal is essentially not actually talking directly to the POS except to tell it that transaction id "xyz"(which only your bank/"card issuer" know is you) was approved, everything else is encrypted between terminal and payment processor and not supposed to be visible to the retailer.

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