Complementary colors are pairs of colors that are of “opposite” hue in some color model. The exact hue “complementary” to a given hue depends on the model in question, and perceptually uniform, additive, and subtractive color models, for example, have differing complements for any given color.
Primary colors are sets of colors that can be combined to make a useful range of colors. For human applications, three primary colors are usually used, since human color vision is trichromatic.
For additive combination of colors, as in overlapping projected lights or in CRT displays, the primary colors normally used are red, green, and blue. For subtractive combination of colors, as in mixing of pigments or dyes, such as in printing, the primaries normally used are cyan, magenta, and yellow, though the set of red, yellow, blue is popular among artists. See RGB color model, CMYK color model, and RYB color model for more on these popular sets of primary colors.
Any particular choice for a given set of primary colors is derived from the spectral sensitivity of each of the human cone photoreceptors; three colors that fall within each of the sensitivity ranges of each of the human cone cells are red, green, and blue. Other sets of colors can be used, though not all will well approximate the full range of color perception. For example, an early color photographic process, autochrome, typically used orange, green, and violet primaries. However, unless negative amounts of a color are allowed the gamut will be restricted by the choice of primaries.