I'm no expert but I think it is a little more comprehensive than that, in addition to the change in the accelerator change I believe it might also change the changing points and swiftness of the shifts. From
our cars do not have a techy sports mode like the M3's I drive system
it's a very simple car and it works bloody brilliantly
you might feel that it changes the shift points due to the throttle not being open 100% all the time when you floor it with sports mode not being on
once sports mode is engaged it allows the throttle to be open as much wider than when it's not in sports mode
so the transmission ecu detects and shifts the gears through throttle input so the gear changes may vary between sports and non sports mode