From a VFD manufacturer's perspective, the question about the type of pump is really about the overload requirement.
There are always exceptions but typically, a centrifugal pump will require a lower overload during start-up than a PD pump. It was common to call them "variable Torque" (centrifugal pump) and "Constant Torque" (PD Pump). From the drive point of view, it is about 'getting the pump started'.
You will see a more meaningful description these days talking about "normal overload" and "high overload".
The Voltage/Frequency characteristic is something used to try and align the benefits of energy saving towards the characteristics of the pump load (pressure) and this is where 'variable torque' terminology comes in. The square load effect of a centrifugal pump is often better served by not applying a linear volts/frequency as the frequency(speed) reduces. This has the benefit of saving more energy.
It is often thought that the VFD 'saves the energy' on a centrifugal pump but in reality all it is doing is following the load demand required by the pump.If you can match that with a volt/frequency curve that is closer to the load on the motor, then all the better.