The goal with fog lights is to throw wide low light with minimal reflection. Reflection is the reason why you don’t use your high beams in the fog. The amber can help with the reflection, but you will find that all modern dogs are clear. The low mounting helps to illuminate the road while keeping the light below the fog layer.
Driving lights are generally spot/pencil beams, or just complete floods. They generally go above the bumper, and should be wired with your high beams. You want to be able to turn them off quickly without taking your hand off the wheel. I have wired mine on past cars this way. The high beam out from the stalk powers the auxiliary switch. The auxiliary switch (when enabled) powers the trigger on the relay.
Beyond all that, fog lights still help with clear driving, and generally don’t piss off oncomming traffic. I love driving lights but fog lights are more versatile.
Edit: As I typed this it is so foggy in Seattle that I can barely make out my neighbor’s house.