Why isn't the saturation current of a photodiode the same as its short circuit current?
Saturation current is the current at which increasing optical power does not produce increasing current. Combined with the sensitivity curve, it establishes the maximum optical power which the PD can measure.

Short circuit current, on the other hand, is specified at a particular optical power - in the case of your link, 100 lux.

So, short circuit current provides an indication of how much current you'll get (for proper detection circuitry) at some specified optical power. Saturation current determines the maximum optical power you can measure.