There are fundamental differences in how these two machines produce colour.
Video displays make their own light. In a completely dark room, you can see them, and when off they look black. They use red, green and blue because those are the colours our eyes are sensitive to, and their purpose is to stimulate those things in your eyes directly so you see the colours they want.
Printers are the opposite. You can’t see a print-out in the dark. The paper with nothing on it is white and if you look at a print-out under any colour of light other than white it looks wrong. You’re mixing inks in order to take white light, bounce it off the pigments, and get the colour you want to bounce back. C, M, and Y are the ideal colours to use for this purpose. If you mix any 2 of red, green or blue together on a monitor, you will get back either cyan, yellow, or magenta depending on which 2 monitor colours you used.
Mixing all 3 ink colours *should* produce black… but in practice, mixing inks causes dilution of the them and it ends up being a grey colour instead. So a separate black ink is used for good blacks instead. It also makes printing in black+white much cheaper since you can just use the one ink type.
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