I think we are missing a term, inverter. It is an inverter, whether solid state or rotary, that can convert single phase 110 or 220(standard household power) to 220 vac 3 phase power. Some, like the Leeson I bought, can change the output frequency so it will act as a VFD. The VFDs we have at the office are all 3 phase in, 3 phase out, with input voltage programmable. Some use 460 vac(500 vac actual) some use 380(on some european equipment).
The attraction of a VFD is that it is the easiest way to control speed of a motor. turn a knob or press a button and the motor speed goes up or down. You do not have to change how the motor is mounted.
The other methods would be belts with different size pulleys, chains with different size sprockets, or gear boxes. these will give you a fixed speed less than or greater than motor speed. they can be complicated, difficult to install, need enclosures (to protect you) , and must be checked and serviced on regular intervals. belts wear out, chains stretch, and gear boxes need oil. I found when designing my disc sander, that to do it properly and have more than one speed, I would pay almost as much for the parts to build a 4 speed belt system (there is a lot more than 2 pulleys and a belt) as I did for the 3hp inverter/vfd.