CABOCHONS
Cabochons are smooth, often domed, with flat backs. Agates and turquoise are usually cut this way, but precious stones such as rubies, emeralds and sapphires may also be. Many stones like star sapphires and moon-stones must be cut this way in order to properly display their unusual appearance.
In the case of a cabochon stone, the side of the stone is usually cut at a shallow angle, so that when the bezel is pushed over the stone, the angle permits it to hold the stone tightly in place.
Just as the angle of the sides of a cabochon creates the pressure to hold the stone in place, so there is an overlying principle in setting faceted stones. If one looks at a side view of a round diamond, for example, one will see that there is an outer edge, called the girdle, and the top angles up from there, and the bottom angles down from there. Faceted stones are set by "pinching" that angle with metal. All of the styles of faceted stone setting use this concept in one way or another.
FACETS
A faceted shape resembles that of the modern diamond. It has a flat, polished surface, typically with a transparent surface that refracts light inside the gemstone and reflects light on the outside.
In the case of faceted stones, a shallow groove is cut into the side of the bezel into which thegirdle of the stone is placed, with metal prongs then pushed over the face of the stone, holdingit in place; cabochons may also be set into prong settings. In both cases, the pressure and the angle of the prongs holds the stone in place.