Shouldn't matter (as best I can tell from the identical wording on the VFD pages you posted) for GND and XGND, but I would swap the GND and XGND so that the PMDX-407's AGND goes the the VFD's GND, and the 407's COM goes to the VFD's XGND. Of course, if you take a meter and measure zero ohms between GND and XGND, it REALLY doesn't matter.
Have you configured the Mach4 spindle speed table? Go to the Mach4 "Configure" menu, select "Mach", then click on the "Spindle" tab. You need to have a valid min and max spindle speeds here, usually in line zero, unless you have GCode that selects a different "gearing" (which I don't recall how to do).
There are two LEDs on the 407. When Mach4 has the spindle turned off, both LEDs should be off. When you try to run the spindle from Mach4, you should see the LED between the ribbon header and the 2-position screw terminal turn on. The other LED, labeled "PWM" should also turn on and its brightness should vary with spindle speed - dimmer at slower speeds and brighter at higher speeds. Do you see these LEDs doing anything?
When you turn the spindle on from inside Mach4, do you see any messages in the Mach4 status line (lower left of the window)? You may have to click on the "history" button if there have been multiple messages.
