Why is it that a credit refunded to your debit card, does not appear on the same day and is not credited back to you immediately, and when you purchase on a debit, that is taken out immediately?

And there is your answer

When you make a purchase and your card is swiped, it sends a temporary authorization or hold to your bank. The transaction will show up as a “pending” transaction almost immediately. But the transaction that was authorized actually doesn’t completely process for perhaps a day or two or three. With a refund, there is no temporary authorization that shows up and needs to be completed. It’s all one transaction. And it processes within a day or two or three after the merchant initiates it.