I hear the term "fixture" and "jig" all the time, but I don't know the difference. Can anyone explain?
The difference can be arbitrary. Or to put it another way the terms might be considered interchangeable.
I don't use the term fixture although I've seen it in print often enough. Jig is one I use a lot and I'd judge it to be much more commonly used by others too, although the type of thing they're used to describe could differ slightly from person to person.
A jig generally refers to a tool or setup, or "appliance" to use an older word, that holds a workpiece in a given way to allow you to work on it more easily. An ideal example is a sharpening jig/honing jig. But particularly with larger shop-built items (e.g. something to facilitate the cutting of tapers on the table saw, or to tilt the workpiece in a pillar drill to make angled holes) you could easily describe such a thing as a fixture. And for something like a bench hook I'm not sure that either word is really right since it can be used in multiple ways, some of which aren't about holding the work, i.e. it can be used just to provide a sacrificial surface to chop on. More on bench hooks in this previous Answer.
To illustrate that the terms may be interchangeable, or nearly so, here's a page on Popular Woodworking. The URL says only jigs, but the page itself is titled Jigs & Fixtures.
And here are two book titles showing the same thing:
But to show how terms can vary, here's a classic book on the same subject from Robert Wearing which uses neither word in the title!
Just in general, terminology in woodworking is often less fixed than we'd like, with minor differences in usage from country to country, in different parts of the US and, as you might expect, with changes occurring over time. Sometimes it doesn't matter much and the context makes the meaning pretty clear, but for the newbie this sort of thing can make things very confusing at times. One of my pet peeves here is with a type of mitre reinforcement properly called a key (also referred to as feathers traditionally) which is frequently now incorrectly referred to as a spline, which is a completely different type of reinforcement.
A fixture holds the piece for machining using work reference points for location.
A jig guides the tool for machining features in their correct location.
An example of a fixture would be if you made a table saw sled made to cut a 23 degree cut 5" from the end of a board.
A jig is something you use to guide a tool for an operation. i.e. a pocket hole jig or a router dovetail jig.
The distinction seems arbitrary, but it lies in how the aid is used.
Carrlane's article "Introduction to Workholding" explains:
Often the terms "jig" and "fixture" are confused or used interchangeably; however, there are clear distinctions between these two tools. Although many people have their own definitions for a jig or fixture, there is one universal distinction between the two. Both jigs and fixtures hold, support, and locate the workpiece. A jig, however, guides the cutting tool. A fixture references the cutting tool. The differentiation between these types of workholders is in their relation to the cutting tool.
That said, many people are not clear on the distinction and commonly call everything a jig. While technically incorrect, most people will immediately understand what you're talking about.