Give or take this is correct. When you check in, they hold (say) $500, and when you check out they are supposed to complete the transaction for the final bill, say $480. The $480 takes a day or two to wind it's way to your bank, and the transaction content in the $480 matches the $500, and the remaining $20 is released. Easy! Of course, getting the hold and the completed transaction to match is not an exact science. I've had cases over the years myself, when the hold and the completion do not match, between them wipe out my available credit.

And yes, there are places that do the hold, and then a completly new transaction for the completion. In some cases, when this has happened, you can call your issuer and get the hold released (manually), or get your limit increased by the hold amount for a few days. If you explain, issuers are generally good at this.

You can be in real trouble if there are finger problems with transaction amounts, and your card is held for $1000 instead of $100. Getting this kind of hold reversed is beyond the knowledge of most vendors/merchants, even if there's a button on their device to cancel a transaction.

And it gets really complicated if your hotel hold is for $500, and then the bill comes to $550. What then? Ideally the hotel will get a hold for an extra $50, before completing the transaction for $550. The extra $50 is a real problem for the industry, since it's almost impossible to connect it to the original $500, which could have been a few days before. There are solutions; some are quite technical, and many places don't impliment them very well.

All of this applies to a credit card, where you have some kind of borrowing facility or credit limit. Using a debit card for hotels and car hire is a whole other world of potential problems...

I'm sure there are other bits of technology that are equally odd