Here is the way we used the two terms:
A FIXTURE is "fixed" relative to the spindle, and is used to locate the part relative to the spindle. No bushings are used to guide the tool. This would be a production set up.
A JIG locates the tool relative to the part, and can be moved or "jiggled" to align to the spindle. Bushings are used to guide the tool. This would be for prototype/short runs or for a repair operation.
Jerry