Differentiation of brightness and whiteness in paper

For most printers and print customers, the brightness and whiteness are interchangeable. However, when explaining the characteristics of the paper, there are some fundamental differences between the two words.

Brightness relates to the percent reflectance of blue light, as mapped at a wavelength at, or about, 457nm. The selection of that wavelength based on the sensitivity of the man eye to blue and yellow light.
Brightness calculates at the time of the bleaching process in removing the yellowness from the pulp.
During bleaching, the curve bend to most blue and violet part at the range of 457nm point. This has also got the measurement of brightness well adapted for measuring the aging.  The reason for this, because of paper yellows with age. Mostly white papers are in the range of 60 to 90% brightness.

Whiteness refers to the degree to which paper shows equally the light of all wavelengths altogether the visible spectrum. A genuinely white sheet of paper will not incorporate one wavelength of light energy more than another.
For example, if a sheet of paper put under a full spectrum light, almost all the light will be reflected back equally, and the paper will appear white. However, if some of the wavelengths of light energy received, the color of the paper will change to the light which was not absorbed but was instead reflected back to the observer. That is why a red sheet of paper looks red in white light because it receives all the other colors and reflects only the red.