In California, the seismic and surveying exams are required for the PE (in Civil). For the SE license, you need an additional 3 years of experience after the PE, presumably under a licensed SE in California in order to sit for the 16-hour Structural Exam. (Western States Structural exam?)
If memory serves, the SE is necessary in California only for high occupancy/critical structures (hospitals, prisons, etc.) and buildings over 160 feet tall in Los Angeles County.
I have heard, but never confirmed, that the original SE requirement in California was political in nature.
States like Illinois require the SE1 and SE2 for anything structural. In most states, the common license seems to be PE, even for "strucural" engineering.
Differences like these are why comity is used rather than reciprocity for subsequent state licenses.
After April 2011, I would imagine that anyone currently authorized to practice as a structural engineer (little "s") would be grandfathered, whether it be a PE, Illinois-type SE, or California-type SE.