A jig is known to be a device that can be used to control other work cutting tools. The jig will make sure that the objects are arranged in their proper positions so that the work can take place properly. Basically, the jig can be used in order to hold the tool while the fixture can only be used in order to keep the items in place, especially during an inspection.
The tools can sometimes be arranged and placed in a certain position with the use of some manual adjustment. Take note that the fixture cannot also be used to guide the tool the same way that a jig can be used.