I've seen VFD, ASD, AFD, inverter, drive, and freq drive all refer to the same thing, right or wrong.
The only thing that bothers me is the last one. I'm not sure, when I hear it spoken, whether the intended spelling is "freq" drive or "freak" drive.
Having lived and worked around these things for 15 years, that last spelling is a bit bothersome!!!
One other note for the original poster. An electronic soft start or reduced voltage starter is significantly different from inverter-based variable frequency drives in that the soft starter is not variable frequency. It is only manipulating the incoming sine wave, either 50 or 60Hz, to reduce the inrush current or the starting torque or both by reducing the voltage to the motor. This makes the start completely dis-synchronous as far as the motor is concerned. Variable frequency drives, on the other hand, start the motor in its normal near-synchronous mode resulting in much higher torque per amp performance.
If your object in softstarting is reduced torque, the difference is small. But if your object is to reduce inrush current, the difference is significant. An inverter will always beat a softstart on reducing inrush currents for the same output torque. Of course, over 10hp, an inverter is more expensive too.