CMYK value of colour doesn't correspond with RGB / HEX
Hey guys, could you please explain me why the colour is so much different when using CMYK code I got (from competition brief) from the colours when using RGB and Hex code? It is same in Photoshop, Illustrator, Indesign, setting CMYK either RGB color mode, trying different working spaces in color settings too. I tested these values on random online CMYK to RGB converters including website color.adobe.com. Everywhere I got result I would expect - the colours are more or less same (I understand conversion between RGB and CMYK might "change" it), but in PS they are so much different - I would say it is green and blue. Why? And why is it working properly online?
What I got in brief

Colours I am getting if setting colour swatch by CMYK / HEX / RGB
Colour picker when I used Hex code - CMYK value totally different 67 / 0 / 58 / 0
Colour picker when I set CMYK code 88 / 0 / 29 / 18 - HEX code and RGB code totally different.
Online converter - If using CMYK code I got I am getting not only the correct RGB and HEX codes but also I see the colour I expect (and which is in the competition brief)
Website color.adobe.com - CMYK code also correspond with HEX and RGB code, also the colour I see is that colour from competition brief. AND this is Adobe website!
I read some threads about colour management in PS and that the CMYK values might differ according settings, but in this case why am I getting the result I would expect online. Is it not weird that the colour is so much different? What am I missing here? It is very confusing. Thanks
Dom
