The other big difference in fog light design is the "spray" of the light.

The easiest (but not perfect) analogy I can come up with is that fog lights are like a flood light and regular headlights are more like spotlights. (Again, I know that headlights are more like a combination of spot/flood but try to see through that for a minute -- no pun intended.)

The M-B fog lights that are part of the headlight assembly or are installed at headlight level still only project the light to the sides and not very far down the road. This also reduces how much light is reflected back to the driver -- especially if you turn off the main beams and only use the fogs.

To answer the original question (which was pretty much answered already), no, foglights don't "cut through the fog." Instead, they simply make the best of the situation by reducing the amount of light reflected back to the driver.

It's still up to the driver to adapt to the conditions accordingly. That would mean slow down so as to not overdrive your reaction time based on the reduced visibility down the road...