"As you walk, the body's weight is distributed more evenly on the foot than when you run. When walking, your weight rolls from the heel, through the ball and continues to the toe in one foot after the other. This gentler, rocking-chair like motion requires your feet to absorb the shock of only 1-2x your body weight with each step. And, during walking there are points where both feet are firmly on the ground, dividing weight. Running, on the other hand (or foot for that matter) requires the support of at least 2-3x your body weight and each stride has moments with neither foot on the ground. With each step, the outer heel absorbs most of the impact before distributing weight through the foot in an S motion through toe off. So what's this mean to your shoes? Basically, it's the old axiom of having the right tool for the job.
Walking shoes are designed with the specific body mechanics and strike path of walking in mind. They are constructed to be more flexible through the ball of the foot to allow a greater range of motion through the roll of the forefoot. They also have greater arch support to protect where the force is heaviest on the foot. Running shoes, in contrast, have more cushioning in the heel–the point of impact–and less protection through the ball of the foot. The amount of heat generated in the running motion is greater, so running shoes also are made with a higher amount of mesh to keep feet cool during exercise."--Brooks Shoes website, http://www.newbalance.com/article_walking_vs_running_shoes.html