In American English there seems to be a distinction between "electric screwdrivers" which look long and slender and generally do not have a "pistol grip", and screw guns which resemble electric drills.If it is a drill that can also drive screws, it's an "electric drill driver" or "electric drill/driver". If it is solely for driving screws it is an "electric screwdriver".
I agree. Though once they have a pistol grip I think they become screw guns.Those straight drivers are ergonomic disasters, which is why modern cordless screwdrivers look like this
You might notice that Packard's screwdriver has a grip that can be twisted to make it a pistol grip.