[1] Depending on the application, different definitions of white are needed to give acceptable results.
For example, photographs taken indoors may be lit by incandescent lights, which are relatively orange compared to daylight.
Defining "white" as daylight will give unacceptable results when attempting to color-correct a photograph taken with incandescent lighting.
Although there is generally no one-to-one correspondence between illuminants and white points, in the case of the CIE D-series standard illuminants, the spectral power distributions are mathematically derivable from the chromaticity coordinates of the corresponding white points.
[3] Knowing the illuminant's spectral power distribution, the reflectance spectrum of the specified white object (often taken as unity), and the numerical definition of the observer allows the coordinates of the white point in any color space to be defined.