Just to add a couple comments (I am referring to the '68 model year in general, not specifically concerning the GT/CS and HCS):
Early in the '68 model year, there was a requirement of a 4V engine (S-code or J-code) for the GT equipment group. This was of course before the release of the R-code (CJ) and the X-code (390 2V) engines. All '68 R-code cars were GT equipped, save for the 50 "135 series" cars built for racing. Of note, the X-code WAS available with the GT option even though it was a 2V engine. To the best of my knowledge, there were NO C-code cars equipped with the GT package (I believe Kevin Marti's data supports this).
Furthermore, in terms of suspension, the GT equipment group (with J-code) got you a 9" rear axle (9" was standard on all big block cars) as well as upgraded (higher numerical) axle ratio, though this was not specifically advertised in any sales literature I have seen. IIRC, 3.25 with J-code and S-code. Standard ratio with R-code was 3.50. For GT with X-code, I believe it was 3.00. C-code cars (GT not available) would have 8" with 2.79 as standard. J-code non-GT would be 8" with 3.00 as standard. I don't remember specifically about S-code and X-code non-GT cars. I also believe that ordering air conditioning had an effect on what axle ratio you got.
To add another layer of ambiguity, I owned a '68 J-code GT coupe that had a 9" with 3.00 gears, and was listed as such on the Marti Report as "optional axle ratio". The car did not have air conditioning. This topic has been discussed at length on the forum before.
Terry