Before pearl farming started, all pearls in the world were natural meaning divers would dive into the lagoon, pick oysters off the reef, bring them up onto land, and then open them hoping to find a pearl inside. You would have to go through hundreds, if not thousands of oyster before finding one pearl. This is why only royalty had pearls back then as they were extremely rare.
During, the early 1900's Kokichi Mikimoto from Japan was the pioneer who invented the cultured pearl industry. He perfected a technique where after you insert a nucleus into the oyster, the oyster will then secrete it's nacre around this nucleus to produce a pearl. Thus was the birth of the cultured pearl industry. So the basic difference between the two is natural pearls don't have a man made nucleus inserted into the oyster whereas cultured pearls do.
It is safe to say that 99.9% of all pearls in the world today, regardless of their country of origin, are cultured pearls. However, the Cook Islands is the only country today that still harvests natural pearls on a commercial basis. I will leave the details of that story for another article.