ALI's restatement of the law governing lawyers: a useful research tool, but not much more than that. Won't be cited much here. Good for comparing the practices of various states.
Admission to the bar is controlled by the Supreme Court. So is regulation. The Board of Bar Examiners and the Office of Lawyer Regulation. BAPR: Board of Attorneys and Professional Responsibility (prior name of OLR). Board of Bar Examiners also tracks CLE, for whatever reason.
The State Bar, like the ABA is private, not related to the Supreme Court, even though there's obviously a lot of interaction.