LC, to answer your question, I’d like to first rephrase it. You wrote:”I asked if that is so, why was it set up one way in EY ( on same day as SA ) and as a separate day in Chutz learetz?”
It’s not a separate day, it is the second day of Shmini Atzeres. It must perforce be different than E.Y. which only has one day, so if Simchas Torah was kept on the fist day in Chu”l, one could ask why that way.
Still, why it’s on the first day rather than the second is a fair question.
The ???? ??????? addresses this, and says it really should have been on Rosh Hashanah, but we don’t want the Satan to figure out when R”H is based on the parshiyos, and once it’s pushed off, we push it off until the end of the Yomim Tovim so as not to have a hefsek of the Yom Tom leining between the end and restart of the regular seder of reading the parshiyos.
http://hebrewbooks.org/pdfpager.aspx?req=14556&st=&pgnum=374&hilite=