To get really basic there are two types: Cathedral and Opalescent. Within these two types is an explosion of choices has happened.
Art Glass – Stained Glass Express
Cathedral is also known as transparent glass. It is clear or tinted. It comes in a vast assortment of colors and surface textures.
Opalescent Glass or semi-opaque has a translucent, milky appearance and lets in less light than cathedral. The glass can be a single color or a combination or two or more.
After this it gets more complex but very, very fun and even more beautiful.
The cathedrals can be antique which can be full antique, drawn antique or scribed antique. There is flashed glass, crackle, reamy, glue chip, seedy, or waterglass. Most of these are about their surface or their texture. It makes for a wonderful variety.
The opalescents combine with the cathedrals by stirring them together and coming up with what we call wispys. Wispys are popular for their depth and luminosity. Then is the combining of more than one opalescent to make streaked glass. This creates great translucent glass with color changes and great visual excitement.
Different manufacturers have expanded by creating baroque, cast glass, catspaw, confetti, drapery, fractures and streamers, or mottled. These differences are from shaping, including things in the glass and creating visual surface shapes.
After that we get into specifics like glass manufactured with a coefficient of expansion for fusing which has shown amazing growth over the last two decades. Then are the glasses with an iridescent coating and the newest glass out, dichroic. Dichroic glass is coated with one or more ultra-thin crystalline layers of metal oxides which enhance reflections at specific wavelengths of light. They say this is done in a vacuum chamber at elevated temperatures. I am quite sure it is really done with a magic wand. The results are pieces of glass that are striking and brilliant colors that change as the angle changes!