Color Calibrating – the display? or the output? Key Basic Issues – help!

I have the Xrite i1Profiler and there are several things I need to understand.

1.) Calibration seems to mean running the software and creating a profile. The profile seems to be located on the computer. Which raises a slew of questions. First of all, it means that you’re not calibrating the screen – you’re calibrating the computer output. Second, it therefore means that the program would have to be run separately for every computer (output device). Third, if there’s no output device that can run a computer program (a DVD player, for instance), then calibration isn’t practically possible. but that can’t be right, can it?

2.) …and fourth, it means that you’re limiting the signal, and therefore not using the hardware potential to its maximum. THIS video has an Xrite expert talking about what sounds like just that – that the calibration can end up in the hardware calibration of the screen. What I want is that: to calibrate the monitor/projector/TV, not to adjust (limit) the output to that screen. I don’t see how this process could be doing that, but I’d like that to be the case.

A. if I have to use my Xrite i1Profiler to calibrate a screen for use with a game player or DVD-player that can’t run software, how do I do that?
B. If I have to use my Xrite i1Profiler to calibrate a wall-sized plasma TV (for example) for use without a player at all, how do I do that?

I’d really love to have a thorough grasp of the principles and possibilities (minus impossibilities) involved. My thanks in advance!