The concept of sport specific shoes is an important one for athletes, even if it is often overlooked.  It is understandably frustrating to need to purchase multiple pairs of athletic shoes, especially if you are an amateur athlete, but the investment is worthwhile when considering the long-term care and upkeep of your body.  For example, consider the different demands that jogging and playing tennis put on your body.  Jogging tends to occur in a straight line (even if you are running cross-country your body moves forward through space).  Tennis, on the other hand, requires you to shuffle sideways like a crab.  The jogger will want shoes that have heel elevation to absorb shock.  The tennis player will need to avoid shoes with elevated heels, which make him slightly unstable when he moves sideways across the court and can lead to ankle injury.  

The difference between running and walking shoes is less pronounced but still important.  When you walk your foot hits the ground with less force.  It also is in contact with the ground almost 50 percent more than when running.  This results in walking shoes having much more flexible midsoles (the part of the shoe between the outer sole and the insole you see when you look into the shoe).  Less cushioning is needed because the foot hits the ground with less force.  And the padding that is used in walking shoes is light and flexible, allowing the foot to smoothly roll from heel to toe.

Most avid walkers can get away with wearing good running shoes.  The drawbacks are that the stiffer sole of a running shoe will make it difficult for walkers to achieve a natural gait.  Also, most running shoes have thick heel wedges (again, for shock absorption and cushioning), which can cause the foot to “slap down” when walking.  In extreme cases, this slap down motion can lead to shin splints or Achilles tendon problems.
Runners, on the other hand, should never attempt running in a pair of walking shoes.  There is simply not enough support for the foot.  Runners need the stiff midsole and thick heel wedge to absorb the shock of hitting the ground and protect the foot from stress.  Feet also pronate (roll inward) to a greater degree when running than when walking and so motion control (features designed to keep your foot in line) is much more important for runners.  Running shoes also tend to be lighter than walking shoes.  This is especially important for the race-conscious runner.  Research has suggested that lighter shoes help you to move faster.  It is estimated that you gain one second per mile for every ounce of footwear that you lose.