White noise is considered random noise; it contains all of the elements that other "color" noises have. It has equal energy at all frequencies. Dithering makes use of white noise; it's used in lots of musical effects, etc.
Pink noise is logarithmic (and thus more pleasing to the sense of hearing), vs. the completely random nature of white noise. Pink noise, in theory, is just white noise through filters. Pink noise's spectrum level is measured down 3db every octave whereas white noise increases 3db. Pink noise, when measured with a real-time EQ at 1/3-octave, will produce a flat response.
In testing mics and any audio equipment, pink noise is more approximate of the frequency characteristics that are pleasing to the human sense of hearing, thus better for EQ'ing systems.