Let's talk about something that drives me nuts. Amethyst is a purple variety of quartz. It is ONLY SHADES OF PURPLE by definition. "Green amethyst" does not exist and we need to start demanding that the proper names be used.
That being said let's run through the colors and the quartz varieties:

Green quartz = prasiolite
purple quartz = amethyst
purple and golden quartz = bi-color quartz, ametrine,
pink quartz = pink/rose quartz
yellow quartz = citrine
brown quartz = smoky quartz
black quartz = black quartz
clear quartz = rock crystal quartz or clear quartz
blue quartz = blue quartz to varieties of greenish blue, and a bright clear pink (almost always synthetic and easily identified by gemologists)

Synthetic Quartz forms in tube shapes due to the machines used to grow them  photo courtesy of WKSU news — Synthetic Quartz forms in tube shapes due to the machines used to grow them photo courtesy of WKSU news

Also a quick word on treated and synthetic quartz. Much of the quartz (colored varieties) you see on the market are heat treated. Heat treatment can enhance or alter the color of quartz. Treatment is difficult to detect, but it is almost always assumed.
Over the years I have also seen a lot of synthetic quartz. It is often times cut into very large stones. There are telltale indicators of synthetic quartz (that are related to the way in which it is grown) that an experienced gemologist can quickly identify.
Synthetic quartz is just as expensive as natural quartz varieties. The is mainly due to the fact that the majority of consumers cannot tell the difference.
As an aside, the market for synthetic quartz has always been strange to me since quartz is one of the most plentiful gemstone materials available.