Why do payment notifications come with different delays?

Question

Payment systems

Shop X. We pay for the purchase with a card - we receive an SMS about the payment within 5-10 seconds. Always.
Shop Y. We pay, we leave and in 2-3 minutes we receive SMS. Also always.
What is it connected with? In my understanding, the processing of the bank that issued the payment card said OK, debited the funds and sent a notification.
It is clear that different stores work through different banks, but to write off funds, the request to the main bank still leaves, because without this, the terminal cannot tell if the transaction went through.

Answer 1

The card can be written off in 2 stages
1) Authorization / Blocking the amount on the card / HOLD
2) Confirmation of purchase
Different banks apparently do this differently

Answer 2

The purchase operation does not directly cause an alert to be sent. It just gets in the queue to be sent. And already another process / equipment from time to time rakes out this queue and sends notifications ... perhaps by draining tasks to the SMS center, which dispatches messages in the same way. Well, the workload, the polling period of the queue - give the corresponding delay.