Neither! In the wires of an electrical circuit, the electrons are always jiggling around. When a circuit is closed to run an appliance or a light bulb, the electrons jiggle a lot and travel through the wire. When the circuit is open, all the electrons just jiggle where they are—kind of like running in place.
Ben Franklin probably did not do his famous kite experiment the way it is usually portrayed. (Franklin never wrote about it himself, and the only description we have of it was written by another scholar, Joseph Priestley, 15 years later.) Franklin believed lightning was a flow of electricity taking place in nature. He knew of electricity’s dangers, and would probably not have risked being struck by lightning by flying his kite during a storm. It is more likely that Franklin flew his kite before the storm occurred, and that his famous key gave off an electric spark by drawing small electrical charges from the air.