Okay, I'm not a banker so there's a good chance I'm the one who's wrong, and I bet the answer changes depending on the specific transaction.
> What you see in your bank account is at the same time real money (as usually talked about), but really really nothing but a bank's promise to pay you some later day real real dollars
We completely agree on this part.
> When I pay coffee shop with a debit cards, exactly what happens is that the bank just tells me that hey, we owe you now less, and we owe the coffee shop a bit more
I don't think this is true. Or, I don't think this is always true.
I can see it being true as a special case: If both you and the merchant use the same bank then sure, probably all that happens is two different IOU tallies are updated.
But I'm currently visiting Turkey, and when I swipe my card Chase definitely does not "owe the coffee shop a bit more", Chase has absolutely no relationship with the Turkish coffee shop I'm sitting in.
And maybe a temporary IOU is created between Chase and whatever Turkish bank the coffee shop is using, but I expect that IOU to be quickly resolved in a few days, when settlement happens. Real money is moved from your bank to the acquiring bank, and an associated IOU shows up in the bank account of the merchant.