There are actually differences between running shoes and shoes meant for walking. :( I guess if you needed to rationalize it, you could say that the walking shoes are kind of like hiking boots, since you wouldn't (technically) be running around everywhere on a mountain or in a really dark cave--you'd be carefully picking your steps and making sure you had a firm, good footing before proceeding. Whereas for longer, flatter stretches or along roads/sidewalks, it'd be better to just run and running in hiking boots or something like that will just give you blisters and ruin the shoes after a while.
:( But really, it's just a gameplay mechanic. Though I never understood why I always had the option to run or walk. Gameplay-wise, why would anyone choose to walk unless it's specifically for a gym like Ecruteak where you have to be careful not to run off an edge? (Any game where the default setting is walk and not run confuses me this way.)