What's the difference of Vs from Vs0 or Vs1? Vs: Stall speed or minimum steady flight speed for which the aircraft
  is still controllable
  
  Vs0: Stall speed or minimum flight speed in landing configuration. 
  
  Vs1: Stall speed or minimum steady flight speed for which the aircraft
  is still controllable in a specific configuration]1


How is Vs different from Vso or Vs1? Is it safe to assume Vs is a generic term involving both Vso and Vs1?
Vs is the generic term.  However, since stall speed varies depending upon how the aircraft is configured (in particular the flaps), we break that down into Vs0 for landing config and Vs1 for cruise config.  In theory, we should list the stall speed for every possible configuration, but it's generally sufficient to list just those two because all others should be somewhere in between.