There are six different SRAM XX S2 derailleurs: bottom and top pull of each of the three dimensions corresponding to the chain ring sizes, 39-26, 42-28 and (not so common) 45-30. I have not seen any model name. Each model is characterized by its features, e.g. SRAM XX FD S2, 39, bottom pull. The bottom pull is also often called down pull
The bolt distance is the same for S2 and S3: 21.7 mm. The measure 22.1 mm is the projection of the bolt distance om the perpendicular on the seat tube axis. This distance is also the same for the S2 and S3. This is why I think that the S3 FD also may fit the frame by just putting a 5 mm spacer between the frame and the mounting plate at the front hole. However, I have not tested the S3 on the frame.
S2 bottom pull is only available as XX, but the S3 bottom pull is also available as X0.