Basically, panning mode one can be thought of as the camera being mounted on a stand. The camera doesn't move, but it can rotate to follow an object. It's the only mode that works well when the camera is position at a distance and zooms in. It gives the motion blur to all objects in the shot, except to the car. Mode 1 can give good results even with a high shutter speed (like, 125 or 250), it all depends on how far away from the object the camera is placed. The closer to the car, the higher the shutter speed can be.
Panning mode two can be thought of as the camera being mounted to a car (or a helicopter). It will travel at the same speed and path as the object, but it does not rotate with it if it were to spin for instance.
Panning mode three can be thought of as the camera being mounted to an invisible stick attached to the object. The camera travels at the same speed as the object, and it also rotates with it. So if you're spinning out the camera will rotate with the car.
Panning mode two and three does usually not give much or any motion blur to objects far away in the background, the exception is when you're shooting an object that is turning. But if you want motion blur in the distance it's almost always better to use mode 1. Mode two and three requires a low shutter speed, usually the lowest (60) to give a good result, but it depends on how fast the car is going of course.