There are two kinds of real, authentic, nature-made pearls:

 Cultured pearls and Natural pearls.

Natural Pearls occur when a particle naturally, or accidentally becomes lodged in a mollusk's shell.  Nature causes layers of nacre to coat and cover the particle. The shape of natural pearls will vary, depending on the shape of the original particle that is being coated.

Natural pearls are the most rare and generally most expensive. Natural pearls are typically sold by carat weight. Most of the natural pearls that are available in these times would be considered vintage pearls.

Cultured Pearl also grow inside of a mollusk. The difference come from the fact that the particle is placed in the shell by humans. The shell is carefully opened and the pear farmer places an object into the shell. The shapes of the final pearl is determined by the shape of the particle that was placed within the shell. In this way, certain desired shapes can be planned. 

Over time the creature continues to cover the particle with more layers of nacre. The length of time that  the particle remains within the shell, the kind of water where it lives, and the actual type of mollusk that "grows" the pearl are determining factors in the size and quality of the final harvested cultured pearl.

Cultured pearls are sold by their size in millimeters.

Saltwater Pearls originate from within a saltwater mollusk. Saltwater pearls may be either natural or cultured.

Freshwater Pearls are those that are grown inside of a freshwater mollusks, living in waters of a river or lake.