Why are different currents through the TVS diode or 8-20 us and 10-1000 us
Disclaimer: I know very little about these but I found the question interesting.

A search for "transil application note" brought up ST AN316.



Figure 1. From the application note it appears that there are two standard test pulses used to test these devices. Note that the average current is taken as the time from the start to the 50% decay point - the second number in the 8/20 or 10/1000 specification.

Reading on:


  Transil peak power dissipation
  
  One of the goals of the Transil is to protect equipment against transient disturbances. The
  duration of these transients is linked to the application where the Transil operates. For
  example electrostatic discharges (ESD) are in the range of tens of ns while industrial strikes
  are within tens of µs, telecom over-voltages, hundreds of µs and automotive surges tens of
  ms.
  
  The performance of the Transil are given in the datasheet for both 8/20 µs and 10/1000 µs
  waves (VCL, IPP), otherwise the curve peak pulse power versus pulsed duration (see
  Figure 3) allows the designer to choose the right Transil for his application.


There are some example calculations in section 5 of the AN. They might be worth a read. I haven't quite figured them out yet.