Can of worms. My understanding is that VFD refers to any control system capable of varying speed and torque, usually through varying the supply frequency and voltage to the coils of an asynchronous AC induction motor. However, it is important to note that a VFD can also control synchronous motors such as BLDC and Permanent Magnet Synchronous Motors (PMSM), although in practice the term is usually applied to control systems for high power industrial AC asynchronous induction motors. It would therefore be incorrect to state "they're really all 3-phase synchronous motors", although some VFD control systems could be seen to emulate synchronous motors with asynchronous motors.
I think it really boils down to being jargon from two different groups, so which term gets used isn't a matter of how the device works as much as it is what the person talking about it does for a living.
At the windings, all motors are driven by some alternating waveform. A classic "DC motor" has a mechanical commutator which turns DC into square wave AC, with the phase leading the motor so the motor turns. Classic AC motors are driven from sinusoidal waveforms. There's a whole theory of DC motors, and an elegant theory of AC motors that goes back to Tesla. Here's the motor family tree.[1]
Then came power MOSFETs. Today you can make pretty much whatever waveforms you want. It took a while for motor designers to learn how to exploit that properly, and for MOSFETs to get small, cheap, and heat-tolerant. Then drone and electric vehicle motors got really good, at the cost of needing a CPU to manage the motor.
