We see red green and blue, but since pigments are about removing light from white light, it uses different colored pigments which each selectively *remove* red, green, or blue from the light. Removing red light gives us cyan (which you refer to as 'blue' above). Removing green gives us magenta. Removing blue gives us yellow.
Since you are dealing with printing, four color process will also use black because it is difficult to get pure blacks by mixing real-life pigments together.
Read through the comments and while they are correct, it's not really the answer to your question.
The difference between light colors and paint colors is the way they mix.
Light (additive color mixing):
Light gets brighter when added to each other.
Think of 3 spot lights. The light gets brighter if the spots have the same target. Combining a red spot, a green spot and a blue spot, produces "perfectly white light"
(Just in theory, as it is fairly hard to produce light of only one exact color)
Paint (subtractive color mixing):
With paint it's the other way around. There are the 3 cleanest colors, or basic colors, Cyan, Magenta and Yellow. As opposed to Red, Green, and Blue when working with light.
Everytime you mix a basic color with another, it gets darker. Adding yellow to cyan, makes it green. Adding magenta makes it brown.
Where I am from, we call this 'breaking the color'.
Adding the basic colors in same parts, would theoretically produce black.
Worked as an offset printer and now working as a graphic designer. Had to use these principles everyday for the last 7 years.
Forgot the answer to your last question:
Our eyes are far from seeing all colors and our printers are far from being able to print all colors
For the eyes:
We see in RGB. So everything you have ever seen, is just that. Everything we can see. What we call colors, are just the wavelengths our eyes can detect. Infra-red cameras basically convert invisible light (infra red) to visible light (RGB on the screen of the camera)
Printers have a really limited amount of colors they can produce, compared to RGB. The problem being that a screen shines, producing nicely saturated and bright colors, while paper doesn't. There are specialized systems to increase the color range of a printer, but even then, it's no match for RGB.