Lathe mandrel is used for supporting hollow workpieces. Lathe mandrels can be termed as Fixture.
A jig is a work-holding device that holds, supports, and locates the workpiece and guides the one or more tools to perform a specific operation.
A fixture is a work-holding device that only holds, supports, and locates the workpiece, but does not guide the tools to perform a specific operation.
Drill jigs are used for drilling, reaming, taping and other allied operations.
Fixtures are the work holding devices, which holds, supports and locates the workpiece but not guides the cutting tool to perform a specific operation.
Post jigs are used for location from a bore.