OK, my dad was an audio engineer, so I can take this one... not speaking to the medical applications.

White noise is sound that contains every frequency in the human hearing range. It is the noise you hear when you tune a TV or radio between stations. It contains each frequency at an equal energy level... that is, every frequency at the same loudness, all mixed together.

Pink noise is useful for doing testing on audio equipment like speakers. The human hear doesn't hear all frequencies at equal level. It is more sensitive to some frequencies than others. Pink noise is white noise that is filtered so that it better represents human hearing. It is filtered so that it contains an equal energy level in each octave of music... "octave" meaning a range of frequencies, where the next octave starts at twice the frequency of the former, just like in music.

If you heard a comparison between the two, you would tell that one has a different "quality" than the other. Sort of like sound through a slightly muffled speaker.

The Wikipedia (www.wikipedia.com) has some more technical definitions if you search "pink noise" and "white noise", and if you go to "colors of noise" there is a list of others and some sound samples if you can figure out how to play them (I'm working on that now )

I am only familiar with the "pink" and "white" varieties.