When a 500 - W electric bulb and a 500 - W heater operate at their rated voltages, the filament of the bulb reaches a much higher temperature than the filament of the heater. The most important reason for this is that

The filament of the heater is much longer and thicker than that of the bulb and hence has greater surface area. It can therefore radiate the same power as the bulb at a temperature lower than that of the bulb. And when they are operated at their rated voltages, the bulb will have a higher temperature.