When you walk, significantly less weight bars down on the ground with each step than when you run. Because of this, a good walking shoe requires less cushioning than a running keds. While you wouldn't want to walk in a shoe without any cushioning, of course, the additional padding you'll likely notice in the heel and forefoot of most running shoes may add more weight than you need. A lighter shoe that still provides some cushioning is preferable for regular use and longer walks, as this will keep your feet comfortable without adding extra weight.
The point of impact changes when you walk versus when you run. While runners strike the ground anywhere from the forward part of the heel through the midfoot to the ball of the foot, a proper walking stride will cause the heel to strike first. Because of this, the type of shoe and the ideal heel height vary by activity. Runners need differing degrees of built-up heels depending on their specific strike pattern, while walkers should look for shoes with the least height differential between the heel and the toe. Be sure to pay attention to the actual heel rather than the shoe's outer sole.
Both running and walking shoes should be moderately flexible; where that flexibility is centralized, however, is what sets them apart. While most running shoes flex at the arch or midfoot (again, this relates to how the foot meets the ground when running), walking involves a forward rolling motion starting with the heel and ending with the toes pushing off the ground. This is best suited to a shoe that flexes at the forefoot.
With a better understanding of the differences between walking shoes and running shoes, you will now be able to find the perfect footwear for your specific needs.