Actually, the way I understand it, the S after the G indicates that is for single pass welding. The G means that it has no other defined properties. One manufacturer could come out with a E71T-GS that uses shielding gas, and another manufacturer could come out with one that does not use gas.
I found another paragraph though, in AWS A5.20 regarding the "G"
A2.4 "G" Classification
A2.4.1 This specification includes electrodes classified as E6XT-G, E6XG-GS, E7XT-G, E7XT-GS. The "G" or "GS" indicates that the electrode is of a general classification. It is "general" because not all of the particular requirements specified for each of the other classifications are specified for this classification. The intent, in establishing this classification, is to provide a means by which electrodes that differ in one respect or another from all the other classifications can still be classified according to the specification. The purpose is to allow a useful electrode - one that otherwise would have to await a revision of the specification - to be classified immediately, under the existing specification. This means, then, that two electrodes - each bearing the same "G" classification- may be quite different in some certain respect.