There are two varieties commonly used, Tellicherry and Lampong. Your everyday black pepper is finely ground black peppercorns. The peppercorns are also used whole and coarsely ground. This is the spice that sent all the early day sailors looking for the Spice Islands over toward the East. In those days it was more valuable than gold.
Black pepper stimulates the appetite and aids digestion.
White pepper is nothing more than the black peppercorns with the dark outer husk removed. It has a milder taste and is used where you don't want black flakes floating around in your white sauce and such. That is, you taste it immediately, and you don't have to wait on the heat as with cayenne. Green peppercorns are unripe black peppercorns. They are preserved in brine and used in a variety of ways.