In the US, we almost always hand the card to stuff and they almost always run it for us. It is only with the widespread adoption of technology like Apple Pay that this is changing in the US. No one is going to hand their phone to the wait staff, so the staff bring a terminal to the table.
Mobile terminals are starting to become a thing, but at least where I live it is very much the exception. Either you pay at the reception desk or hand your card to the staff at the table, depending on where you eat.
Is this a real thing? Germany is horribly behind on payment options, but even we have mobile terminals that you yourself handle.