What is difference choosing credit or using PIN on a debit card?

Answer 1

The fees that the merchant pays to the bank are different.

For you, there isn't always any difference.

Answer 2

My bank allows 2) debit transactions a month free but charge $ .50 each for anything after that.  Having vendors run the debit card as a credit avoids those fees.   

Watch the "Fee" section of your bank statements, they hide it in there!

Answer 3

The former usually requires your signature.   The latter requires you to enter you PIN.

The merchant is charged differently to process each of these transactions.