Basic difference: a fixture holds/guides the stock; a jig holds/guides the tool.
A fixture is a device used to hold stock in place while you work on it. A vise, by this definition, is a sort of universal fixture. Assignment #1, first week of class: design a fixture for a brake disc. Classical solution: first square the stock, then use a generic square fixture to hold the stock while you drill the radial hole pattern, then make a fixture with the same hole pattern and bolt the stock to it while you machine the profile (grooves/holes, circular outline, etc.). And yes, this is metalworking, not woodworking, but the definition ought still to apply.
A jig may be a fixture in that to do its job it must also secure the workpiece. But the primary role of the jig is to guide the tool, whether or not it also secures the stock. In the modern manufacturing world where you can have CNC machinery the notion of a jig is somewhat outdated. You just tell the tool where to go, and how fast, and it happens. In our world, where we have generalized hand-controlled tools, jigs take the form of pocket-hole devices, router templates, guide rails, etc. that constrain the motion of the tool to the path we wish it to follow.
A pocket-hole jig is an example of a jig that doesn't also need to be a fixture. You fasten the jig to the workpiece and it guides the tool, but the stock can be held any way necessary or comfortable. Some dovetail jigs also function as fixtures because they hold the stock in place (since you'll have both hands on the router) as well as guide the router through a profile.
"Fixture" would be the proper term associated with holding stock for use in a table saw. Many CNC systems also work by moving the stock, so "fixturing" need not be interpreted as "holding the workpiece stationary" but rather by holding the workpiece firm in a certain coordinate system of the tool. If a tool works by moving a platform -- with workpiece attached -- along a path relative to a stationary cutting bit, then a "fixture" would ensure that the workpiece does not move relative to the platform.
--Jay