Besides the obvious differences in ball position and slightly more upper body tilt with the driver, I feel that the difference is primarily the
quantity of left forearm rotation
(for righty) because of the difference in length and therefore a flatter swing plane for the driver. The flatter swing plane takes a little more work to get the butt of the club pointing to the target line (behind the ball). It has taken me quite some time and suffering to understand this and put it to work on the course. My irons were always better until I got a couple of driving lessons - then my irons suffered a bit.
I then came to this conclusion and put it to work successfully: besides the obvious setup differences, the driver simply requires more forearm rotation and slightly more shoulder turn.