As to your original question.
I also have a Star Super SM 380
Mine has wooden checkered grips, but I have seen pictures of many with plastic grips that had a thumbrest. GCA'68 required X number of "points" to qualify for importation, the thumbrest was something that helped add points.
Also, for those that don't know, the "Super SM" had a takedown lever on the right side. Rather like on a Beretta 92, the earlier "SM" 380s disassembled like a 1911.
I read somewhere that there were 12,000+ Super SMs made. One person described them as "Ultra rare, not sure I agree about the "Ultra" part
Nice little guns, not too tiny though, I CCW'd mine for a while, then upgraded to 9mm Shield.