An easy way to tell them apart is by looking at the epidermal ridges/skin lines. If the lines move around it then it is a wart. If the lines go through it, its a corn.
While 'over the counter' treatments may work for most warts, they don't often work on plantar warts because you are only treating the surface of the wart while most of it lies under the skin.
A podiatrist can help bring the wart to the surface by using a combination of acids, deflective padding & regular debridement. Cutting plantar warts out surgically can actually cause more problems because you are left with a scar that becomes painful to walk on.
With professional help, plantar warts can be eliminated.