Amethyst is the purple variety of Quartz, and Citrine is the amber-yellow colouring of it - the colour is determined by the minerals present in the stone when it it being formed.
For instance, iron and aluminum give the purple colour to Amethyst. (There is a fascinating article on Amethyst on Wikipedia).
Citrine is generally heated Amethyst or Smokey Quartz - heating it changes its colour. Citrine and Amethyst present in the same stone are known as "Ametrine."