Here is how I teach it (condensed since you already understand PWM theory)
A standard VFD (lets call it a Scalar Drive) puts out a PWM pattern designed to maintain a constant V/Hz pattern to the motor under ideal conditions. How the motor reacts to that PWM pattern is very dependent upon the load conditions. The Scalar drive knows nothing about that, it only tells the motor what to do. If for example it provides 43Hz to the motor, and the motor spins at a speed equivalent to 40Hz, the Scalar Drive doesn't know. You can't do true torque control with a scalar drive because it has no way of knowing what the motor output torque is (beyond an educated guess).
A Vector Drive uses feedback of various real world information (more on that later) to further modify the PWM pattern to maintain more precise control of the desired operating parameter, be it speed or torque. Using a more powerful and faster microprocessor, it uses the feedback information to calculate the exact vector sum of voltage and frequency to attain the goal. In a true closed loop fashion, it goes on to constantly update that vector to maintain it. It tells the motor what to do, then checks to see if it did it, then changes its command to correct for any error. Vector drives come in 2 types, Open Loop and Closed Loop, based upon the way they get their feedback information.
A true Closed Loop Vector Drive uses a shaft encoder on the motor to give positive shaft position indication back to the microprocessor (mP). So when the mP says move x radians, the encoder says "it only moved x-2 radians". The mP then alters the PWM signature on the fly to make up for the error. For torque control, the feedback allows the mP to adjust the pattern so that a constant level of torque can be maintained regardless of speed, i.e. a winder application where diameters are constantly changing. If the shaft moves one way or the other too much, the torque requirement is wrong and the error is corrected. A true closed Loop Vector Drive can also make an AC motor develop continuous full torque at zero speed, something that previously only DC drives were capable of. That makes them suitable for crane and hoist applications where the motor must produce full torque before the brake is released or else the load begins dropping and it can't be stopped. Closed Loop is also so close to being a servo drive that some people use them as such. The shaft encoder can be used to provide precise travel feedback by counting pulses.
Open Loop is actually a misnomer becuase it is actually a closed loop system, but the feedback loop comes from within the VFD itself instead of an external encoder. For this reason there is a trend to refer to them as "Sensorless Vector" drives. The mP creates a mathematical "model" of the motor operating parameters and keeps it in memory. As the motor operates, the mP monitors the output current (mainly), compares it to the model and determines from experience what the different current effects mean in terms of the motor performance. Then the mP executes the necessary error corrections just as the closed Loop Vector Drive does. The only drawback is that as the motor gets slower, the ability of the mP to detect the subtle changes in magnetics becomes more difficult. At zero speed it is generally accepted that an Open loop Vector Drive is not reliable enough to use on cranes and hoists. For most other applications though it is just fine.
This is all done at very high speeds, that is why you did not see Vector Drives as available earlier on. The cost of the high speed mP technology has now come down to every day availability.
"Venditori de oleum-vipera non vigere excordis populi"