The jig is kind of tooling that guides the cutting (or machining) tool. The most common type of jig is the drill jig, which guides the drill bit for creating holes at desired locations.
The fixture is the tools which holds the work piece with the machine bed precisely at the desired location. The fixture also reduces the nonproductive loading, unloading, and fixing time of the work piece. A fixture is a work-holding or support device used in injection manufacturing industry.
Jigs allow you to be super precise and careful in your plastic mold design layout and plastic mold design once and then get repeatable results consistently with relatively less effort. For example, if you attach two narrow boards to a bigger piece of plywood, painstakingly making sure they are at a right angle to each other, then you can just clamp two boards to them and be sure they will be square. You can do this over and over again after being careful in your craftsmanship just the one time.