Vs1g is the lowest speed, at which the airplane can maintain 1g, i.e. level flight. It corresponds to the Cl max
Vs is the lowest speed attained during stall testing of the airplane. The pilots were able to reach this speed lower than Vs1g, but the plane was already losing altitude.
The way I understand it, the certification rules were changed at some point, and new airplanes are required to base their performance on Vs1g, whereas airplanes certified earlier were referencing to Vs.
However, this puts the new airplanes at a disadvantage, as Vs1g is higher than Vs. To counter this, Airbus managed to convince the certifying authorities, to allow for lower margins during performance calculations (eg. Vref is 1.23*vs1g instead of 1.3), because the airplane is speed protected anyway....
P.S. strangely enough, ATR-42/72 also use Vs1g and lower safety margins, even though they are a conventional plane, not speed-protected