Your profile when calibrating the monitor is just a tool to correct your monitor. It's hardware related, not software.
Think of colors in wavelength, you don't have to know exactly what wavelength they're, just they exist as wavelength, analogue values.
Digital images have no colors, they've digital values. A value of 255,0,0 will tell the monitor to produce a color red with 100% of it's capacity. It would be nice if we all experience that color the same way. Monitors are using a colorspace that defines within what wavelengths it will produce colors. Look for a horseshoe and pay attention to the wavelength.
I'm not an editor and don't have PS. But this article might bring you further
http://regex.info/blog/photo-tech/color-spaces-page1. Read them all and open the links at the end to see if there's something more for you.
I hope I gave you some hints for further thinking.
George