In a nutshell, Variacs (Variable AC) are for adjusting the AC voltage.
VFD's vary the frequency, thus changing the on off duty cycle from 60 times per second to other ratios.
A variac is great for a resistive load - light bulb, a soldering iron, or a PM motor. It will not work on most larger motors or electronic devises.
For a grinder or shop equipment only a VFD and a matching motor will work (or go with a DC motor)
Stacy