\"Pharmacy\" is a predominate word used to describe a place where you pick up your prescriptions and it is not necessarily a store. What I mean by that is that there can be (and is) a pharmacy inside a Kroger or Albertson\'s grocery store (and you\'d say I need to go to Kroger Pharmacy or to the pharmacy at Kroger to pick up my prescription).
\"Drugstore\" is a type of a convenience store that carries all kinds of goods, but mostly cosmetics, beauty products and of course all sorts of \"over the counter\" (i.e. those for which you don\'t need a prescription) drugs and health products.
Each drugstore also has a pharmacy where you can fill in your prescription. The most popular drugstore chains (at least in my neck of the woods) are: Wallgreen\'s, Eckerd\'s and CVS, but they\'re certainly more than just a pharmacy.