I don't really understand what your question is.
All a control valve can do is apply a variable resistance to flow. This results in an increased pressure drop relative to flowrate.
What control function you want the valve to do is irrelevant, the valve doesn't know this or care.
So it is the data and cases you put into the data sheet which impact on the choice and sizing of the valve.
If you're controlling flow, then the boundary cases are normally max flow with lowest differential pressure allowed, lowest flow with highest differentia pressure possible and then maybe a "normal flow case with "normal" flow and pressure drop
For pressure control which can be pressure upstream, downstream or differential then the boundaries are similar if reversed,
So controlling on a fixed downstream pressure the boundary cases are:
lowest upstream pressure at max flow
highest upstream pressure at max flow
highest upstream pressure at min flow
So in short, forget about the "designation" - it's a control valve.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.