The profile saved by your calibration software is your Monitor Profile and absolutely nothing else..
It has absolutely nothing to do with your working color space or your printer (target) profile.
Monitor profiles are absolutely device-dependent, that means it only applies to your particular monitor unit and nothing else, not even an identical monitor of the same brand and model.
Your working space should be a a device-independet color space, such as ProPhoto RGB, Adobe RGB, sRGB, etc.
Your printer profile, also called target profile, is a totally device-dependent profile for your specific combination of paper/ink/printer.
You need to do an awful lot of reading on Color Management, a subject some of us have spent a very long time studying before we grasp it. A good place to start would be here:
Thank you for the link, I will take a look at it and hopefully get a better idea. I tend to get "obsessed" so I tend go over board.
Here's the thing: the color management chain requires two profiles. A source and a destination. One single profile means nothing, that's like one hand clapping. A profile is just a description; it doesn't do anything. The relevant part is the translation from one into the other, IOW the relationship between them.
That's why you need to have 1) a document profile, 2) a monitor profile, made by your calibrator, and 3) a printer/paper/ink profile, installed with your printer software.
For specifics, see above.