Modern Clear Sheet Glass is called 'float glass' because it's created by literally floating a ribbon of molten glass on a bed of molten tin.
This is an interesting and informative video on the making of float glass though, curiously, it does repeat the myth of glass as a super-cooled liquid that will flow over time, making antique windowpanes thicker at the bottom.
The video was shot at the Pilkington company, who received the patent for float glass in 1959.
Float glass is rarely used in stained glass windows. It's considered too uniform in appearance and therefore too cheap looking. I know of some studios that only use it for heavily painted, stained and enameled pieces. They like the toughness of the glass and the fact that there is no machine or handblown texture to show through - and the cheap price doesn't hurt either. Note that if you do paint on float glass, you must be aware that enamel paint and silver stain react differently on the 'tin side' compared to the 'non-tin side'. The tin side is the side which was in contact with the tin in the process of floating the glass, and this tin will dull colors, especially transparent enamels. For instance, a nice gold pink transparent enamel could end up a rusty red instead. Unfortunately, you can only tell which is the tin side by looking at each side using ultraviolet light.