The "Ask Alyce" question of the day:
What's the difference between black and white pepper?
Well, both are berries from the same tropical plant. The black are picked when not quite ripe, and dried. There are many varieties available, from the common plain "black peppercorn" to Tellicherry or Szechwan, both of which are more flavorful than the common grocery variety.
The white are ripe berries that are soaked in water, with the hull, or dark outer covering, rubbed off before drying. Although there is a difference in taste (I personally prefer the taste of the black, a bit more pungent than the white), the bigger difference is aesthetic: many chefs think the white pepper looks better than black on light-colored dishes, such as cream sauces, poached or baked fish, or light meats.
As long as we're talking about peppercorns, we might as well talk about the green ones, which are the very under-ripe berries, usually preserved in brine, although they are also available freeze-dried. And pink peppercorns aren't peppercorns at all, but from a completely different plant. Pungent and slightly sweet, they too are available either brine-packed or in the more common freeze-dried form.
Whatever your choice, all peppercorns are best freshly ground. I have individual little peppermills for the table at home, with a mixture of all four types of peppercorns. For cooking, I have one mill with black and a smaller one with white peppercorns. Whatever form your peppermill takes, please make sure to clean it frequently!