Quartz is, after feldspar, the most abundant mineral on the earth crust. There are two big families within the quartz minerals: the macro-crystalline, mostly transparent varieties and the micro-crystalline (or crypto-crystalline), which are translucent or opaque. The opaque range includes agate and jasper.
Pure quartz or rock crystal is the colorless transparent variety. Colored quartz goes by a lot of different names such as amethyst, citrine, rose quartz, and so on. More on rock crystal @ http://dunebeads.com/en/april-s-birthstones-about-innocence-love-and-shhh-rock-crystal
Tourmaline exists in a rainbow of colors and from milky white to black. Black opaque tourmaline is also called Schorl (from the german Schürl or Schörl). More about the lucky stone of October http://dunebeads.com/en/october-s-birthstones-about-hope-opal-and-tourmaline
Rutilated quartz is a transparent rock crystal with rutile inclusions. Black Rutilated quartz is a pure quartz which contains a unique pattern of needle-like black tourmaline.