Local Meetings are called Monthly Meetings because they meet for business once a month. There are local Meetings that are under the care of Monthly Meetings and these are generally referred to as Worship Groups.
Most Monthly* Quaker Meetings are members of Yearly Meetings and those Yearly Meetings are associated with one of the Quaker umbrella organizations. Birmingham Friends (monthly) Meeting is part of the Southern Appalachian Yearly Meeting & Association (SAYMA) which is associated with Friends General Conference (FGC) while Chatham Friends Meeting in Snow Camp N.C. is part of the North Carolina Yearly Meeting which is associated with Friends United Meeting (FUM)
As with other denominations, there have been disagreements that lead to splits in the organization. As a result, there are three Quaker umbrella organizations. FUM, FGC and Evangelical Friends Church International (EFCI).
Although Friends agree on the basic premise that "there is that of God in everyone," they do differ on how they conduct their worship services and the acceptance of traditional Christian theology. FUM and FGC are united in their opposition to war and in their support of the Friends Committee on National Legislation (FCNL) and the American Friends Service Committee (AFSC). I know very little about EFCI and their positions regarding war or their support for the above mentioned wider Quaker organizations.
The FGC Meetings are usually unprogrammed worship, meaning they have silent worship but if anyone is lead to speak out of the the silence they do so. In addition to meeting for worship, there is often a regularly scheduled discussion time on a variety of topics.
Most FUM Meetings are more traditional in their beliefs and worship: they generally have a church service with a shorter (20 minute) period of silent worship, paid clergy, and are more Biblically based in their approach to theology.
The only Quaker Meetings in Alabama are associated with FGC and are unprogrammed Meetings, with the exception of the Fairhope Meeting which was originally associated with Ohio Yearly Meeting but, I believe,it is now only loosely associated with Ohio Yearly Meeting.
Quakers, with the possible exception of the Evangelical Friends, do not subscribe to a creed or statement of belief. From the EFI web site, it would appear that they do subscribe to a statement of belief and they appear to be very much like other mainstream evangelistic denominations.
* Although Monthly Meetings meet every 1st Day (Sunday) they are designated as Monthly because they have monthly business meetings.