SS-I = USDM GT
SS-II = USDM GT-S
SS II "Super Strut" = GT-S with a double wishbone front and rear suspension.
Here is a translated qoute form the Japan Toyota website. "it loads double wishbone suspension to the rear on the front." Also if you look at a JDM TRD catalog they have a coilover set for the "super strut" and the front shocks look nothing like what we get here. A fellow Celica owner here tried to order it and had to send it back because he couldn't use it for the USDM GT-S.
As stated above, the differences between the USDM and JDM versions are mostly suspension-related. People often talk about the horsepower differences and ask, "How does the Japanese 2zz engine make 190 HP and the US 2zz make only 180 HP?" However, that is kind of a misnomer, since the Japanese 2zz-powered Celicas actually make 190PS, not 190 HP. Since 1 PS = 0.986 HP, then the Japanese Celicas actually make about 187.3 HP (using American standards of horsepower).
Also keep in mind that many dynos of American 2zz engines seem to indicate that Toyota slightly underrated the US-published flywheel horsepower of 180 HP. Stock US Celicas seem to be making slightly more than that. Factor in the slightly higher octane gas sold in Japan (which allows the Japanese ECU to run slightly more aggressive/advanced ignition timing), and you can see that the power difference between US-spec Celicas and Japan-spec Celicas is very minimal.