Runners who use minimalist/no shoes generally use a forefoot/midfoot strike (the ball of the foot hits the ground first), while those with thickly padded shoes are usually heel-strikers.
Heel strikers tend to run more upright, with the heel landing well forward of the runner's center of gravity, while fore/midfoot strikers lean more foreward, with the foot landing almost under the CG. It's like you are always just 'falling forward', with your feet catching you from falling on your face. It takes some getting used to, but the effect is much lower impact than heel striking.
The reasoning is twofold: 1) If your foot lands well forward of your CG, you are effectively retarding your forward progress and increasing the force traveling up your legs, and 2) By striking with the heel, you remove the flexing of the foot and calf muscles as a shock absorber, and the force travels directly up the leg - right up into your knee. The padding in the heel of the shoe (and it's always the heels that are heavily padded) don't make up for the loss of the foot/calf system as a shock absorber.
You can run using a fore/midfoot strike with a thickly padded shoe, but the thick heel just seems to get in the way.