You need both.
The ground radials are there to act as a counterpoise to the radiating element (the 102" whip). They make the ground plane under the antenna to give it a nice radiation pattern.
On a car, the metal roof or body would act as the ground plane under the antenna, the 3 radials under your antenna serve that purpose.
The ground cable and ground rod serve as a lightning ground. Lightning is searching for a path to ground. If you don't give it one, it will find one. Usually through your antenna, feed line, radio, you, your house, your dog, and every piece of expensive electronic equipment it feels like destroying. By giving it a path to reach ground, it will help give it a place to go. Doesn't mean it won't go through you, your dog, your new TV, etc, but most of it will go to the ground rod. The ground rod will also give static electricity that can build up from wind, rain, etc a place to go, rather than through your radio.
So, you need both.