DC motors, AC motors, and Kv
In both PMSM and BLDC motors, the speed and frequency are indeed locked to each other.  However:


The PMSM has a fixed input frequency in the sense that it's not affected by the motor itself and therefore a fixed speed in relation to that frequency.  Speed is controlled directly by frequency; the voltage and current limits are simply high enough to provide some headroom so that it doesn't stall under load.  (but not so high as to fry the motor)  It's also designed to run directly from AC power, which is sinusoidal, so it needs a sinewave inverter to control the speed well.
The BLDC has a controller/inverter that varies the frequency to match whatever the motor is doing at the time.  Think of a brushed motor that uses transistors instead of brushes, and you're really close.  Therefore, the BLDC has a Kv.
It's designed to run exclusively from an inverter, so the flat-topped trapezoid is more transistor-friendly and allows the inverter to be cheaper yet still just as effective.


These two kinds of motors are actually interchangeable in a pinch; they just won't work as well.  Higher noise, less efficient, etc., unless the inverter can drive both and you tell it about the change.

There are two other things to know about motors in general:


All motors have inductance that increases their impedance with higher speed.  AC impedance is somewhat analogous to DC resistance, except that there's now a phase angle involved that makes things more complicated.  (There's also a phase angle between a PMSM's rotor and the driving voltage that varies with load and contributes to the impedance.)  The increased impedance lowers the current for a given voltage, which reduces the torque.  This is why a stalled motor draws maximum current and produces maximum torque.
All motors generate a voltage while they're running that is proportional to their speed and locked in frequency.  This back EMF works against the voltage being applied to further reduce the current.  Kv is theoretically the rate of back EMF vs. speed.  (it would require a mythical free-energy source to go beyond that)