I'm confused by the overlap between these two features of Mach4.  Does calibration performed in the probing screen affect the touch screen?  When would you use one feature over the other?

Monitoring, I've wondered this myself!

Does calibration performed in the probing screen affect the touch screen?

No, the in screen method and the touch module are 2 totally different things.

When would you use one feature over the other?

In a nutshell........... when one suits your needs or way of working better than the other.

The biggest difference is the in screen probing was meant to be used with actual probes. The Touch module will work with a probe but not as nice as the built in probing. But, the touch module will also work for those using touch plates and /or tools instead of a probe. Without a probe with give built in, doing a fast find (which the built in screen probing does) can damage the tool / part / touch plate.

I also tried to make the Touch module a good example folks could study and learn by or even modify to their own liking. It was also good practice for me writing it with a useful purpose.