Its a really good question, and the answer reveals a lot about what goes on in the magnetic field outside a wire that is carrying a current.
Since the current runs down to the socket end on the hot wire, and returns on the neutral, the magnetic fields around the wires are in opposite directions as you look down the wire. If the wires had no space between their centers (not possible), then then fields would cancel exactly and there would be no electromagnetic radiation detectable outside. The more they are separated, the more the fields won't cancel and the part that isn't cancelled gets radiated outward.
So why don't you feel the magnetic attraction like an electromagnet, even weakly?
Well electromagnets use DC current. They force magnetic north to point in a constant direction, just like a bar magnet. But an extension cable carries AC current, so the field that does radiate is changing direction 60 times a second. This acts like a de-magnetizer instead of like an electromagnet, because it is constantly changing the direction of North. If you were to lay an extension cable on top of a cassette tape long enough, the weak radiated field would degrade/(partially erase) the recording. But it would not attract a nail. The nail will have some internal electrical eddy currents induced, which in theory, heats the nail ever so slightly.
If you want to heat the nail a great deal, then you separate the conductors and wrap one of them around the nail many times, to multiply the effect by the number of wraps. You also multiply the current by some factor to again multiply the induction effect by that factor.
And now the heating effect is multiplied by both factors, and you have made an induction heater.