Both the CSV and VFD hold a constant pressure while varying the flow rate to match the usage. We have been replacing VFD's with CSV's for over 26 years now. You can get up to 10HP with a regular single phase motor, and working with a CSV it would be much less expensive and work better than a three phase motor with a VFD to convert to three phase.
A CSV can also make a VFD system more reliable. The VFD is just used to convert single phase to three phase (if you only have a three phase motor). Then the set point for the VFD is set higher than the set point of the CSV. That way the VFD just makes the pump go to full speed, and the CSV varies the flow and holds the pressure constant. In this way the VFD is either at full speed or it is off, which is a little more dependable than letting the VFD vary the pump speed.
But usually the VFD is used without a CSV. The CSV is just used to replace the VFD when people start having problem with the VFD, which they always do.