Fixture: A device designed to hold, support and/or locate a component for a processing operation of some kind to be conducted, but they do not guide a cutting (or other) tool.

Jig: A device designed to hold, support and/or locate a workpiece and to guide a cutting tool or similar processing operation around or along a specific path or location.  Jigs are usually used to control the location or motion of another tool.  A jig’s primary purpose is to provide repeatability, accuracy and interchangeability in the manufacturing of a component.