So this means that CMYK and RGB and not fully compatible?
Color Management is what tries to make them compatible.
In theory where the color spaces overlap you can produce the color out of either space. There are however many many many factors why this doesn't happen. Starting with the first problem that RGB without a tagged profile isn't a fixed colour at all, its just 3 numbers. So if I assume it is sRGB or Adobe RGB I'm starting from 2 quite different colors and I haven't even started the conversion to cmyk, which you can imagine has a whole lot of options/strategies you can choose from.
One more thing, once you have converted to cmyk don't think you can get back to the same RGB values because you can't (other than cmdZ) because the math is lossy.