What does "case" mean exactly for this three-prong photodiode?
FDS1010 DATA SHEET

FDS100 data sheet here


  Why doesn't the FDS1010 have a "case"?


Case provision in the FDS100 is more a matter of happenstance than necessity.
 The case is provided for convenience of mounting.
 As they have the case there they make provision to connect it electrically, but a case is not an inherent necessity for photo diode operation. 


  Should I treat "case" as a ground and wire it to my potentiostat's ground? 


The case can be grounded.

In the FDS100 the case is not electrically connected to the diode in any way but can serve as an electrostatic shield when the diode is used in a "floating" application where neither terminal is grounded.

For example, diode response speed and linearity can be improved by applying reverse bias. In this case the diode "floats" above ground and the 3rd lead is grounded.
 As shown below (diagram from datasheet). 






  The FDS100 and FDS1010 are both attractive candidates for my application


It's worth noting that as well as increased area, the FDS1010 offers better response linearity with wavelength (but less response at the very deep UV end of the range). The FDS1010 has about 7 x the active area and ~= 5 x the sensitivity, but frequency response is about 8 MHz compared to typically 35 MHz for the FDS100. Graph from datasheet - 


FDS100 FDS1010.jpg