What is the difference between pump VFD and VSD?

There is no difference between VSD and VFD in terms of what they are designed to do. There might be some differences based on specific internal components/construction and how they achieve the goals.

Variable Frequency Drives (VFD): are drives work on changing the frequency of motors; they can be used with AC motors only.
VariableSpeed Drives (VSD): are drives work on changing the speed of motors by varying the voltage supplied to them; they can be used with both AC motors and DC motors.

Reference source:

http://www.gohz.com/difference-between-vsd-vfd-asd-afd

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