A CRT monitor will need to 'turn on' Red/Green/Blue components to display a color(because the screen is 'black' by default. For a printer, the paper is already White(which is a mix of all other base colors), so it needs to 'turn off' some light components and 'leave on' those representing the desired color.
Each color system is capable of representing a certain group of colors(a "color space"), but none of them is able to actually cover all visible colors. These color spaces do not completely overlap, so there will always be colors that can be represented in some color systems while not having a direct correspondent in others. So converting from a color system/space to another is a rather complex problem.
There are many color systems defined, but they can be grouped into "additive" and "subtractive" systems:
some devices (e.g. Monitors) use "additive" color systems, like RGB(Red, Green, Blue): the base color is Black, and you can "add" red/green/blue to obtain other colors. You obtain "White" by using the maximum amount of all three components.
other devices ( printers ) will use "subtractive" color systems(like CMY or CMYK), where the base color is "White", and you "mask" some components to obtain other colors. In CMY, you get to "Black" by mixing the maximum amounts of all three components.