I would recommend that you read up on Color Management and Color Science to get an understanding of why colors can/may look different. Especially read up on “gamut”.
Those formulas are only there for when you don’t have a proper ICC-based color management system in place. They will NOT provide accurate conversions.
I think I have a good understanding of color management, and I am very aware that different devices may have very different gamuts and may also give very different colors for the same input device colors.
But, again, here I am talking about pure device colors, and thats why there should be no differnece in defining a color in (device) CMYK vs (device) RGB. In device space the colors are of course device dependent, but the same color should still come out the same on the same device (in this case, my screen). The two are still exactly the same color, only "opposite" (subtractive vs. additive), and as long as we are in device space there is no device information (like ICC-profiles) involved. Its like defining weight in Pounds or Kilos; there is a direct conversion between the two.
Thats why I wonder why the colors come out differenly in the PDF when I view it in a PDF-reader, like for example Acrobat.
I was thinking that maybe a PDF reader assumes that a Device CMYK will be reproduced in print and "simulates" a print by using a standard CMYK outputprofile (like for example Euroscale Uncoated) while it assumes that a Device RGB will be reproduced on a screen and therefore uses a standard RGB outputprofile (like for example AdobeRGB or sRGB).
Again, the thing is that pure colors in DEVICE space look different on the same device. Is it the PDF-reader that is "simultaing" paperprints for CMYK-colors? ...or is there something else here that I am missing??
(EDIT:...the CMYK color is of course a lot less bright than the RGB in my PDF, and thats why I thought maybe the smaller gamut of a printer on matt paper is simulated, creating a lot more "dull" color...)
As you point out, these are DEVICE DEPENDENT colorspaces, which means that the viewer can setup the device any way that it wants. In the case of Adobe Acrobat/Reader, we use the "working spaces" defined by the user via ICC profiles to be those spaces. If you want reliable color, don't use device colorants. That's why all the PDF subset standards (PDF/X, PDF/A, PDF/E, etc.) all require the use of device independent colors.