There are several types of stained glass. I'll describe a few for you.
You've probably seen those church windows with milky looking glass in swirling colors on a lighter background - that's opalescent glass. It's often used for lampshades because you can't see the lightbulb through it. Most opalescent glass is dull or garish. There is some that is quite beautiful, but it's expensive, so you usually see the cheap, dull stuff.
Then there's cathedral glass - it's translucent colored glass, often has a bumpy surface on the back side, so it often looks like a colorful shower stall. It's fairly cheap and looks it.
Fusible glass is a palette of colored glass that has been tested for expansion and contraction, so after it's fused together, it doesn't expand at different rates and shatter.
In my opinion, glass that's blown on a pipe with someone's mouth on one end and molten glass on the other end is the loveliest glass of all. The bright colors are vibrant without being garish, and the pale colors are subtle and gorgeous. Because this is hand made glass, every square inch is textured differently from any other square inch. This mouth blown glass is called "Antique Glass" because it's made in the old way. This is the glass I primarily use in my windows.