Is there a commonly-accepted distinction between the either power drill or electric drill and electric screwdriver, whether semantic, dialectic, sociolectic, or something else? — For myself, power drill seems most unmarked, followed by electric drill and then electric screwdriver. To me, they all mean the same thing, namely a gun-like device which accepts bits of various types, either for drilling or "screwdriving". However, there have been times (admittedly mostly by non-native speakers of English yet also by some native speakers) when I ask:
Me: Have you got a power drill?
Someone else: No, I'm sorry.
Me: (surprised) Well, I can't screw this in by hand: The material is just too hard.
Someone else: I think I might I have an electric screwdriver somewhere.
Me: (confused) Okay... thanks.