I wanted clarification on the first radio call to ground. As far as I understand, if you are moving your plane at all (specifically to a run-up area), you must make a call. This is true whether controlled or uncontrolled. But what if my plane is already parked in the run-up area and I do not need to move? Let's assume I had my pulled my plane to the spot. Would I still need to make a radio call (and if so, what would it entail)? Or would I just need to make that call once run-up is complete and I am ready to taxi to the runway?

What I had learned the initial call to be was "XX Ground, XXXX. Requesting taxi for run-up." Is this what I should still use?

Thank you!

And say what exactly? “Hey ground, request taxi to where I am now?”

Nobody cares about your run up, just call when you’re ready to taxi for takeoff.

Depends where the normal run up area is. On a big ramp, I would taxi away from other parked planes, point my tail away from other aircraft, and do the run up. No call needed unless the ramp is controlled (which I have never encountered). Then call, ready for taxi.

On a crowded ramp, there is no room for that, so ask on initial call up to ground where they want you if unfamiliar. (or better, especially at a busy airport, ask the FBO or fueler)

Sometimes its another spacious area partway along the taxi route where your not blocking anyone. Some airports have a designated run up bay adjacent to the departure end of the runway. Request taxi from ground, go right to that runup bay, then call tower when done and ready to go, or as instructed.

Questions like these are best left as a discussion between you and your instructor. If there's a lot of factors to consider, depending on where you are and what you want to do - it's easier to answer and demonstrate in the moment. You should ask your instructor for these clarifications if they are still fuzzy. In any case, keep radio calls simple: Who you're addressing, Who you are and where you are, and what you want to do. "Winnipeg Ground, (callsign), Apron 2, Ready for taxi - VFR to Brandon."

If you are talking to ground control then you are at a controlled airport. The first thing you need to know is what part of the airport pavement is controlled. Ramps, Aprons and taxiway's may or may not controlled. If the taxiway is identified by a sign eg "A" then you must contact the ground controller before entering it. Where there is an uncontrolled ramp or apron the boundary between it and a controlled surface should have a sign or painted note indicating who to contact before crossing the boundary.

To the OP I would suggest that your issue is not what call to make but a less than complete understanding of airport ground ops. I unfortunately see this a lot in flight training where students do things because that is what the instructor told them not because they understand why the action is required.

Finally there can be times particularly with private ramps or taxiways, where it is not entirely obvious as to where the the controlled surface start so it is if course always a good idea to clarify the situation with ground control is you are not sure.