In the US, almost universally, they take the card away. Swipe it somewhere in the back -- without a PIN. Then bring back a receipt for an inked signature, which is supposed to the be the alternative to a PIN.
Oh, and you put the tip in on that receipt, and they go back and do a second entry of the tip (sometimes incorrectly, almost always higher when incorrect.)
Worse - the transaction alert -- if you get one -- is the pre-tip amount. Makes no sense.
FYI if they enter the final amount incorrectly you can dispute the charge with your credit card provider. It's probably a stronger case if you kept your own copy with the final amount that you wrote down.
If they took the card away, how would you enter the card's PIN? That's why places outside the USA do the swipe on the table.