The description given above about the incoming AC to a VFD being rectified to DC and filtered smooth is exactly correct.
The output inverter stage consists of six solid state switches, usually IGBT's, two for each motor lead. As a result, each motor lead can be connected thru these switches to either the + side of the DC bus or the - side. The voltage on this DC bus is relatively constant being equal to the peak value of the incoming AC voltage. So, for 460VAC, that would work out to around 660VDC.
The inverter output section of the VFD is not sending anything resembling a sine wave to the motor since the only thing these switches can do is turn on or off. The result is a high frequency train of pulses all of which have a peak voltage equal to the DC bus. The only thing that varies in these pulses is the amount of time that they stay on, or their pulse width. Hence the term, Pulse Width Modulation or PWM.
This pulse train alternates back and forth between being positive pulses and negative pulses thus attempting to create the alternating phases of an AC wave. It is up to the inductance in the motor to take these high frequency variable width pulses and reformulate in the current something that approximates a sine wave. This sine wave, with varying degrees of distortion is what the motor runs on. Note that a sine wave never does appear in the voltage--it's nothing but a train of pulses.
That explains why the motor squeels and sings on inverter power. Those pulses are actually disturbing the magnetic components of the motor and creating noise that you can hear. That also explains why motors tend to run warmer on inverter power--they are busy integrating these pulses as well as trying to produce torque in the shaft.
Since the VFD electronics determine the switching times of the inverter switches, it is relatively easy to create the equivalent of variable voltage and variable frequency so the motor will develop torque at variable speeds.
These's a lot more to it than that, but that's the basics.
Hope that gives you a start on understanding VFD's.