"Smelt Quartz" is not quartz at all -- it is glass, which is made from melting quartz in the presence another compound (called a flux) which lowers the melting temperature. Glass is not crystalline, whereas quartz and other minerals (with few exceptions) are crystalline. Most people can't tell the difference, but glass is optically isotropic (doesn't polarize light) whereas quartz is anisotropic (polarizes light). Glass also has a lower density, which you might be able to detect by its heft, and "smelt quartz" usually has unnatural looking streaky patches in it.
"Smelt quartz" does not have any of the properties of true quartz.
"Smelting is a heat treatment for separating metals from their ores. The ore, often with other ingredients, is heated in a furnace to remove non-metallic constituents. The metal produced is later purified."