It's sort of like Anglicans in the US, who can be ECUSA, REC, AMiA, or part of a South American or African group.
A fair sized city in the south is going to have several Southern Baptists, an American Baptist if there are a lot of yankees, perhaps an independent baptist church, and an assortment of Black baptist churches.
Thanks for the explanations. I grew up in the deep south and always saw the different signs on the churches, but never really thought of them as distinct or that different.