The two generally control two different aspects of the image projected by the lens. Focusing sometimes has the effect of changing "zoom" a little as well, however its purpose is different. To keep it simple:

• Focus adjusts the Focal Plane
  • The focal plane is the thin plane of reality that is focused clearly on the imaging medium
  • Focusing moves this plane nearer or farther from the camera's sensor/film
• Zoom adjusts the Angle of View
  • The angle of view is the breadth of the scene projected by the lens
  • Wide-angle lenses tend to capture very broad scenes (large angle of view)
  • Telephoto lenses tend to capture very narrow scenes (small angle of view)

Focusing in the past used to be achieved by moving the lens itself (i.e. in a large-format view camera) forward or backward (away/towards the imaging medium). This often results in changes to the angle of view as well, since the total focal length of the lens can change via extension...sometimes by a lot. In modern camera lenses, focusing may be achieved similarly...many cheap lenses focus by moving the front or back (or both) lens elements. Higher quality lenses tend to use an internal floating focus group, an internal group of lens elements who's sole purpose is to focus the image. The benefit of internal focusing groups is that the physical length of the lens stays the same, allowing you to minimize the amount of "zoom shift" that might occur when focusing.