Time- and space-resolved fast framing photography was employed to study the discharge initiated by runaway electrons in air and He gas at atmospheric pressure. Whereas in the both cases, the discharge occurs in a nanosecond time scale and its front propagates with a similar velocity along the cathode-anode gap, the later stages of the discharge differ significantly. In air, the main discharge channels develop and remain in the locations with the strongest field enhancement. In He gas, the first, diode "gap bridging" stage, is similar to that obtained in air; however, the development of the discharge that follows is dictated by an explosive electron emission from micro-protrusions on the edge of the cathode. These results allow us to draw conclusions regarding the different conductivity of the plasma produced in He and air discharges.