Running shoes are WAY better than walking shoes. They are also more lightweight and have more cushioning in the soles to absorb the impact from running. If you like Nike running shoes, Kohl's has good prices on them. That's where I get mine from. Sometimes I get women's and sometimes I get men's in a smaller size if they don't have the size and color I want in women's. the styles are usually the same.
Best ever. Seriously. My orthopedist recommends running over walking sneakers because they are more flexible, and usually have a wider toe box. They are also very stable. A lot of money for the ones I purchased, but they last me well over a year and I don't spend much on shoes anyway. And my feet feel a lot better too.