Actually, as a Baptist, I can tell you that there are substantive differences between the SBC and Cooperative Baptists. One of which involves women in ministry. The Baptist faith & message statement prohibits (or at least heavily discourages)women in ministry or deacon roles. That’s one reason my church became more moderate, plus we wanted autonomy in where our missions dollars were spent - not dictated by the SBC.
The CBF always complains that it is about autonomy and political power within the SBC, but when you boil it down to gravy, it's about the authority of the Bible and its clear teachings--women in the clergy is one of many departures from orthodoxy...