Most so-called green quartz in the market are actually heat treated amethyst. There are other green stones that look like green quartz and they are green tourmouline, green obsidian and green calcite. Most green stones are heart chakra stones and they have both general healing abilities especially for heart related ailments. Green stones in Chinese folk lore are considered as wealth stones (example green jade, emerald...), and they are more for wealth accumulated through business and career rather than windfall. For those doing retail business, I would normally advise them to place a green stone in their cash register.
There is a type of quartz that contain green rutiles (or Chlorite) and they do look like green quartz if the concentration of rutiles in the stones are unusually high. Phantom green quartz also looks like green quartz.
Blessings
Diamond