First Baptist simply means (generally speaking) that the church was the first Baptist church in the area.
Calvary Baptist is just the name of the church.
If you live in the Southern US, almost every baptist church will be either Southern Baptist or National Baptist. However, there are many, many additional baptist groups. In the Northern US and out West, you'll see both of these two groups plus a heavy influence of American Baptists.
To clarify for a moment, all baptist churches are 100% independent. What I mean is that they do not belong to a higher organization like Catholics (who have parishes, dioceses, etc. up to the Pope), Presbyterians, Methodists, etc. Each baptist church runs itself and may even have its own unique beliefs.
However, baptist churches may choose to join an association. Often there are church associations at the state level. There are also church associations at the national level (the Southern Baptist Convention or the National Baptist Convention, for example). To join the association, a church must agree to certain beliefs. Typically there is also cooperative giving towards mission work from all churches in the association. (i.e. pooling funds to send missionaries out, etc.)
There is not much difference in theology between Southern Baptists and National Baptists. Because both sprung up in the Southern US during and after slavery, sadly, these two groups divide on racial lines (with some people of each racial groups attending the other, but it tends to be a minority). National Baptists are typically African American. Southern Baptists are a bit more likely to be a mix of Caucasian, African American and Latino.
Here is a list of all Baptist groups in the US from Wikipedia.
Major Baptist organizations in the U.S.
The Handbook of Denominations in the United States identifies and describes 31 Baptist groups or conventions in the United States.
[4] A partial list follows. (Unless otherwise noted, statistics are taken from the
Baptist World Alliance website, and reflect 2006 data.)
[2]
- Alliance of Baptists: 100 congregations, 60,000 members[3]
- American Baptist Churches USA (ABCUSA): 5,800 congregations, 1.4 million members
- Baptist General Convention of Texas: 5,700 congregations, 2.3 million members
- Baptist General Association of Virginia (BGAV): 1,400 congregations, 400,000 members
- Baptist General Conference: 1,000 congregations, 140,000 members
- Conservative Baptist Association (CBAmerica): 1,200 congregations, 200,000 members
- Cooperative Baptist Fellowship (CBF): 1,900 congregations, 700,000 members
- General Association of Regular Baptist Churches: 1,400 congregations, 130,000 members[4]
- National Association of Free Will Baptists: 2,000 congregations, 200,000 members[5]
- Old-Line Primitive Baptists
- Progressive Primitive Baptists
- Southern Baptist Convention (SBC): 44,000 congregations, 16.3 million members[6]
- African-American Baptist groups:
- National Baptist Convention of America, Inc.: 12,000 congregations, 3.1 million members
- National Baptist Convention, USA, Inc.: 33,000 congregations, 8.5 million members
- National Missionary Baptist Convention of America: 300 congregations, 400,000 members
- National Primitive Baptist Association: 1,500 congregations, 250,000 members[7]
- Progressive National Baptist Convention: 1,200 congregations, 2.5 million members
- Independent (non-aligned) Baptist churches
I would just suggest trying out some of the Baptist churches in your area one by one and seeing what you think. Each will be slightly different because of the church members as well as the pastor. Some may be more traditional; some more contemporary; some more charismatic--it all varies.
Here are a few more relevant links:
Wikipedia: Baptists in the US:
http://en.wikipedia.org/wiki/Baptists_in_the_United_States
National Baptist Convention:
http://www.nationalbaptist.com/index.cfm?FuseAction=Page&PageID=1000000
Southern Baptist Convention:
http://www.sbc.net/
American Baptist Association:
http://www.abaptist.org/home.shtml
I hope this helps!

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