I had always thought that "equalize" meant that each channel ended up with a uniform distribution. However, that's not what I'm seeing in Photoshop- values are redistributed, by the histogram isn't linear.
Running Gimp's Equalize command gives histograms that look like parabolas.
Only Picture Window Pro gives the expected uniform distribution.
Why is such a simple command implemented differently?
The reason why is because "equalize" needs a "what is important"-type qualifier (a "metric"). Although in the literal sense, you are right, but there are several types of equalizations.
E.g. check out this paper. You can see several types of equalizations there:
but there are many more.
Equalization can be on pixel values, on perceived contrast, perceived brightness, on local or global areas, etc.
If you expect a uniform distribution over bins, the software uses dynamics compression/expansion aside of histogram equalization. Is it good or bad? You will get an "even-er" look but may loose contrast edges or details.
EDIT: Just adding some more info.
Check out the last image on Wikipedia. The histogram is wavy, what is important there is the cumulative histogram, which shows a nice distribution over the entire dynamic range. One way to use equalization.
More information on adaptive histogram equalization, especially on contrast-limited adaptive histogram equalization.
