One key element in photography is color and a whole language has developed to help describe colors. The challenge is that color is not finite. It’s a human perception so this language of color includes both objective and subjective pieces.
One of the first to write about color theory was Leonardo da Vinci in the late 1400’s. Others, including Sir Isaac Newton, built upon these early writings. In fact, Newton developed one of the first wheels presenting the theory of primary colors.
Today, color theory is quite complex as it tries to keep up with an ever evolving digital technology. Two important, but often confused, elements in color theory today are Color Space and Color Gamut.
Color space defines the colors that are available in a specific subset of a color model. In photography, we generally use an RGB color model, but there is no single RGB color space. Instead, different color spaces have been developed, each creating a unique subset of colors of the RGB color model.
There are many different color spaces but the most common with photographers include sRGB, Adobe RGB, and ProPhoto RGB.
An analogy that veils the complexity of color spaces is one of a box of crayons. Any box of crayons gives you a finite number of colors with which to draw. The larger the box of crayons, the more colors you can use. And, essentially, the greater the variety of colors, the greater the potential for beautiful images. (Yes, I know a good artist can create stunning images with a small box of crayons but let’s debate that later.)
When your camera creates a color image, it assigns values for each of the colors based on a specific color model. If you shoot sRGB, then all the values used are part of the sRGB color space. This doesn't mean that a color defined within your image can be reproduced by a specific printer or display.
A color gamut represents all the colors that a particular device can produce. The key here is that a color gamut is unique to devices that create color.
A color gamut is also a subset of colors within a color space. You may have an image that uses the sRGB color space, but some of those color may fall outside of the color gamut of the output device you are using.
For example, a computer monitor and an inkjet printer can both create colors. The monitor creates the color with lights such as light emitting diodes (LED). The printer lays down ink that reflects the light that shines upon it.
The family of colors that each can produce is quite different so they each have their own Color Gamut.