I'd also make the obvious observation, that the speed and torque requirements of a cordless drill and an electric screwdriver, and, specifically, the ability to start turning while under load, are quite different.
Your practise may vary, but I find it is always better to turn the drill on before I attack the piece of wood with it, but the screwdriver works better if you put the tip of the screwdriver into the slot or star-shaped hole on the end of the screw, before you turn the screwdriver on.