From here: 


  For the US market:



  "Rabbit" - base model. These are only available very early so are pretty rare.



  "Rabbit C" = Rabbit Custom. This is just one step up from the base model (Which are just called "Rabbit")



  "Rabbit L" = Rabbit Lux (translates to "Deluxe".) One step up from Rabbit C.



  "Rabbit LS" = Rabbit Luxury Special. One step up from Rabbit L.



  "Rabbit GL" = Rabbit Grand Lux. Another step up in terms of features and options from Rabbit LS. I think only sold in '83-'84.



  "Rabbit S" = Rabbit Special. Weird model with red trim, I think '82-only, that was pre-GTI. It went away when GTI was introduced in '83.



  "Rabbit GTI" = Rabbit Grand Turismo Injection. Explanation not needed.



  Most commonly, Rabbits are fuel injected gasoline motors - their badges say "Fuel Injected" on them (except GTI, where the I stands for "injection" it would be redundant.) There were also Rabbit Diesel and Turbo-Diesel ('83-'84 only) enging options which are each also noted on the badge. If the badge doesn't say anything regarding the engine option (IE: Fuel injection/GTI/Diesel,Turbo Diesel) then the engine is just carburated.

This implies that in the A3 line the "base model" is equivalent to a "Grand Lux" Rabbit. Speculating here, but it seems GLS would be "Grand Lux Special" and GLX, "Grand Lux eXtreme".