There are many different types of gemstones, and knowing the different categories can help a collector or enthusiast expand his repertoire greatly. Some precious gemstones are so unique in chemical composition and crystalline structure that they fall into their own categories, while others can be collectively lumped into one. Here are the major types of precious and semi precious gemstones:
Diamond - diamond is it's own type of gemstone, and is well known for being the hardest naturally occurring substance known to man. Diamonds are primarily high-carbon crystals that were fused under extremes of pressure and heat.
Diamonds themselves aren't especially rare, with thousands being mined throughout the world every year; however, large diamonds of high quality are extremely rare, and it is these which are well known for setting the standards of diamond gemstones as the world's most precious stone.
Corundum - this is the second hardest type of gemstone, and is primarily defined as being composed of aluminum oxide and various trace minerals. The trace minerals create different types of corundum, and perhaps the two most well known examples of this type of stone are rubies and sapphires. Rough corundum isn't used as a gemstone, but is used as an industrial strength abrasive element due to it's tough nature.
Chrysoberyl - this is the third hardest gemstone, and while it uses aluminum oxide as a base element like corundums, it has high quantities of beryllium mixed in with it. Appearance wise, chrysoberyls often come in a green to yellow shade, though their appearance is best known for having the tendency to actually change color somewhat under different types of lighting. Cat's eye and alexandrite are two common chrysoberyls used in jewelry.
Quartz - this is actually one of the most common types of mineral in the world and comes in a wide variety of colors. It's main tendency is to form in hexagonal shapes and it makes an excellent prism if unflawed.
The main reason quartz can still be categorized as a valuable gemstone is that, while it IS easy to find quartz stones, finding a large, perfect, and unflawed quartz crystal of jewelry quality is extremely rare. Some examples of quartz gems commonly used in jewelry are onyx, amethysts, citrines, and carnelians.
Beryl - this is a stone well known for it's beauty and has elements in common with both chrysoberyl and quartz. It's basic chemical composition is similar to chrysoberyl, with beryllium and aluminum prevalent but mixed in with other trace elements. It's basic crystalline structure, on the other hand, is closer to quartz, being hexagonal in nature.
At it's simplest, beryl is actually transparent, while it's other colored variants include emeralds and aquamarines. It can come in yellow and red shades as well, and these are referred to as "red" or "yellow" emeralds.
Jade - this is one type of gemstone originally lumped into the same category as beryl. The main reasons for this are because both can be mined in similar places and they possess similar textures, opacity, and appearance (just different colors).
Later on, chemical analysis showed that the elements which made up the different forms of precious jade, namely nephrite and jadeite, were different from beryl completely, thus earning jade it's own category among gemstone collectors. Jade based stones are often composed of calcium and magnesium elements.
Feldspar - this is a unique type of gemstone whose base material is tectonic in nature. It is often found in areas of high geographic instability like earthquake faults and volcanic chains. Feldspar's basic chemical composition is made up of very common elements found deep inside the earth's crust.
What makes it valuable as a gemstone is the same factor that makes a diamond much more valuable than a lump of coal that would normally contain the same elements as diamond. That is, with sufficient heat and pressure applied, the tectonic elements fuse together to make a rare red gemstone known as feldspar.
Organic Gemstones - the most famous examples of this are pearls and amber. Basically, organic gemstones are ones which occur naturally in organic sources as opposed to mineral sources. Pearls are formed from oysters, while amber is a yellow stone formed from fossilized tree sap. While not gemstones per se, organic gemstones are still used heavily in jewelry so are included in this list.