Yes, rear fog light is for safety, when there is fog or heavy rain, it makes it easier to sight the car in front. Rear fog light shines much brighter than regular taillights. Actually the rear fog light has a separate switch. There are different regulations, when to use front fog lights and rear fog lights. In Estonia it is allowed to use rear fog light only on highway, but front fog lights may be used for daytime driving everywhere, but then it is forbidden to use headlights at the same time. Using front fog lights with headlights is allowed only, when there is low visibility due to fog or rain.