The first diagram is legal in most states --- the second is NOT. Second is great for making a clean get away from a stick up at your local Tom Thumb or WaWa at night. Believe the code says the front and rear running lights must be on when the fog lights are on. In the fog you'd surely want the rear running lights on - plus you don't want to leave them on when car is parked.
Road Rule 217 states that drivers must not use front or rear fog lights unless driving in fog or other hazardous weather conditions that cause reduced visibility. They must be switched on separate from the main beam (high beam) and dipped beam (passing) headlights. Jan 5, 2016