White peppercorns come from ripe, red berries that are soaked after harvesting to facilitate removal of the red skin.

Black peppercorns are obtained from unripe green berries that are left to ferment for several days before drying.

Green and pink peppercorn are simply the same as above, but not treated.  You may find green peppercorn pickled or dried.

You can use them interchangeably, however the white has the advantage of being less visible in the food, but personally, I prefer the black pepper because it tastes more pungent and aromatic.
Did you know this about the peppercorns?