Color theory is both the science and art of using color. It explains how humans perceive color; and the visual effects of how colors mix, match or contrast with each other. Color theory also involves the messages colors communicate; and the methods used to replicate color.
Tints, tones and shades are variations of hues, or colors, on the color wheel. A tint is a hue to which white has been added. For example, red + white = pink. A shade is a hue to which black has been added. For example, red + black = burgundy. Finally, a tone is a color to which black and white (or grey) have been added. This darkens the original hue while making the color appear more subtle and less intense.