How to correctly save a file to CMYK and PMS formats?

This is what I was looking for, an answer to another user on GraphicDesign Stack Exchange:

CMYK can produce less colors than RGB, which is why many "equivalent" colors can seem dull or washed out. Pantone can produce brighter colors since they use specially-mixed inks, however it is often more expensive to use spot (Pantone) colors for printed materials. In an ideal world you'd have a color that works well in all 3 systems, but that is not always possible.

So what to do? What I'd do is find a CMYK color you like (because CMYK is the hardest to get right), find the RGB/Pantone equivalents, going by eye (with a well calibrated monitor and pantone swatches).

So, why is so difficult to answer a simple question???

Ok, I will search for "color management" on Google to see what comes. However, my question is about a more practical thing. When we download a brand guidelines manual, we will find there a default CMYK color code to be used by whoever wants to use that logo wherever they do. So, the person or people who created that manual DOES NOT KNOW MY MONITOR's COLOR CALIBRATION, and neither other people`s monitor.

My point regarding my question is: how would you pick a CMYK color to your, let's say your logo, to be used WORLDWIDE doesn`t matter anyone's monitor whether they know if it's calibrated correctly or not? I think I could be more clear this time.

The website Adobe Color does not use any color management. It uses very simple calculations based on ideal theoretical CMYK inks to convert between RGB and CMYK.

It is best to use the colormanegement as provided in Illustrator Photoshop and InDesign.

I agree with Monika; you need to learn more about how color models and color management work. Your entire "2nd point" illustrates this—your expectation of convert-from-xxx-then-convert-back-should-be-the-same-xxx will never be true. Even when your color management settings (which is how color conversions are governed) are a known entity, conversions to/from the disparate systems HEX, RGB, CMYK, PMS, etc. are not based on direct relationships. Conversion is always a compromise of sorts, and additional conversions only add to the "mutation".

Perhaps this can help get you on the right track:

https://www.youtube.com/watch?v=y7UxglZCD1M

Nobody knows which color management is set up in Adobe Color.

So whereever you live and whichever output method you use those values might or might not work.

Also: For a lot of RGB colors, you won't find a match in CMYK. Please learn about color management and printing.

Using Pantone colors without having the swatches book is like walking blindfolded. When doing the conversion you should at least set up color management on your computer correctly and then do the conversion on your own system with settings you know.