Person gets the wrong card handed back to her? That's a "mixup".
Person just sticks the card back in their wallet and walks out with it? I could see that happening. Mixup.
Person quickly walks across the street to the nearest mall and starts running up a tab on it?? Fraud. And pretty stupid to boot, especially since they just likely swapped cards, and the real cardholder has their name.
The mall isn't off the hook either for doing credit card transactions without following basic procedures: matching signatures, asking for ID on larger transactions, etc.
Back in the early 1980s, I worked for a drugstore chain as a cashier/manager trainee. Our average transaction size was maybe $40 or so. It was not only SOP to check the signature and ID, but we additionally had to look up the card to make sure it wasn't listed in a do not accept/take possession bulletin which came out in paper format about every week or so and was placed at every register.
If the transaction was over $100, we had to have it called in as well. I kid you not. This was a high volume store about 40 miles east of downtown LA.