Corns and warts are two common foot conditions. The difference between these two conditions is that corns are concentrated only on the feet while warts can appear all over the body.
Corns occur when there is localized high friction pressure on the bony prominences of the foot. The foot then responds to the added pressure by thickening the skin in that area to protect itself. Such skin pressure causes an inadequate blood circulation in the skin to cause corns. A corn doesn't itch or bleed. You feel no pain if your pinch it. The only pain you may feel from a corn is direct pressure when you stand up or walk.
On the other hand, a wart is not related to friction. It is a skin condition caused by the human papilloma virus that enters the skin through breaks or openings or other direct body contact with the virus. Corns are not infectious while warts are contagious and hence should be treated as quickly as possible.