Lightness, also called value (Munsell) or tone, is defined as a colors placement on a brightness scale ranging from black to white. The Munsell color space, for example, divides the lightness axis, called value, into ten equidistant steps. Lightness, on the other hand, stems from the HSL (Hue, Saturation, Lightness) and Lab color spaces where it is used similarly to Munsell value only in percent. The HSV (Hue, Saturation, Value) color space speaks not of lightness but of value and uses the word value differently than Munsell does. In HSV value ranges from black to not white, but to the fully saturated color. Paints can be made lighter or darker by adding white or black, but that also reduces saturation. “Tone” is an obsolete term that stems from darkroom photography to denote the lightness of a specific area of the print. Yet “tone” is still used in art where light and dark are built up with charcoal or similar drawing medium
In digital photography lightness can be calculated simply as (r+g+b)/3. However, that does not take into account that green is brighter than red and blue darker than red. In the IUV color space the relative brightness of the color channels is taken into consideration, like this: i=(76*r+150*g+29*b)/256; It approximately says that green is twice as bright as red and red is 2½ times brighter than blue.
In painting the term “tone” denotes an intermediate between gray and pure color. “Tint” denotes a mixture of pure color with white and “shade” denotes a mixture of pure color with black. In the real world tint and tone are not a simple as the theory implies, because though they do not have color in themselves, when white or black are mixed with a color, the color changes hue. In other words, black in mixtures behaves like a blueish color. For example if you mix yellow and black you don’t just get a darker yellow, but you get a darker and greenish yellow. Similarly will an addition of white make a color appear colder.
In software you can digitally create tints and tones by converting from the RGB color space to IUV or Lab color space and raise the L (lightness) channel as described above. This will not alter the hue of the color as when you mix pigments with black or white.