Pure Red Coral: The rarest of corals, pure red coral, or Corallium rubrum, is used mostly for jewelry making. Also known as fire coral or oxblood coral, the hue of the stone is a deep, rich red. The stone has been over-harvested, and because of this there is not much natural red coral left. Red coral lives deep in the ocean and is highly desirable. It's often set with other natural gemstones, especially turquoise, and looks stunning when paired with yellow gold. Much of the red coral on the market today is dyed to achieve the rich hue.
Simulated and Reconstituted Coral: When coral is reconstituted, it means that one piece of coral is made of other natural ocean material, small pieces of coral or coral powder that have been soaked in binding agents, pressed into one solid piece and then re-cut to be set into jewelry. Reconstituted coral is usually dyed to achieve a more uniform appearance. Simulated coral is not real natural coral at all, and can be made from any number of man-made materials, such as plastic or resin, to resemble the real stone.
Black and Angel Skin Coral: Black coral, which is no longer available commercially, used to be harvested in Mexico and the Caribbean and can still be found in pieces of vintage jewelry. Black coral grows in the shape of a tree and doesn't become black until after it's harvested. It's extreme rarity and small size--it takes lots of black coral to get enough to make just one piece of jewelry--means that it can't be used commercially any more. A pink coral called Angel Skin comes from the South Pacific and is often used for jewelry. It's rarity makes it expensive, though generally speaking, it's of lower quality than the more popular red coral.
Bamboo Coral: Bamboo coral grows in many areas of the ocean and is used widely in jewelry, either dyed red or in it's natural state of marbled hues of green and brown. It is mostly used to create coral beads.