You can use the website
to get an idea of how people with color blindness see the world. The most common kind, by far, is deuteranopia.
My grandfather was totally color blind and could not distinguish colors. This is true of about one man in 40,000. He led a perfectly normal life, and actually did not realize he was colorblind until well into adulthood. People with color blindness develop an enhanced ability to see small differences in grays and in textures, and often name colors correctly through clever use of cultural cues.
About 8% of all men have a form of partial color-blindness. By far the most common kind is an inability to distinguish reds and greens, while retaining the ability to distinguish between blues and yellows. Color vision involves perceiving both hue and "saturation." Saturation is a measure of how pure the color is. The blue in a rainbow, or the blue of the color #0000FF on a computer screen, is completely saturated. The blue sky is not very saturated.
A person with normal color vision lives in a three-dimensional color world (two dimensions of hue and one of saturation).
People with the commonest red-green color blindness live in a two-dimensional color world. It is very different from "black-and-white," and much richer.
To them, a bright, saturated green looks different from a bright, saturated red. However, they are seeing a difference in saturation, not hue. To them, a bright, saturated green looks the same as brown ("brown" is the name for a dark, unsaturated, red-orange).