I'm kind of stuck in the middle of all of this (attending a Baptist seminary), so I'll try and give my thoughts, with an extremely abbreviated history.
This is something that's been in the making for over 25 years. In 1979 there was a group of men who decided that they were going to attempt to take over the Southern Baptist Convention with a fundamentalist agenda -- that is, they decided that if you do not believe what we believe, then you're wrong. Over the next ten years, they slowly gained control of the SBC, firing seminary presidents and professors who promoted academic freedom and who were not on their side. They put people in the seminaries who would teach exactly what they wanted them to teach (quote from Adrian Rogers: "And if we tell them to teach that pickles have souls, then they must teach that pickles have souls!" ). Along with this they gained control of all committees of the SBC.
There was opposition to all of this, from the so-called "moderates", but it couldn't be stopped. Texasag73 -- you nailed it. Being a Baptist means congregational autonomy and freedom of the believer, and now professors, pastors and missionaries were required to sign the Baptist Faith and Message and agree to teach according to it. I know you're Catholic, so this might sound like a good idea, but this is not a Baptist principle. One pastor I know claims the only thing he will ever sign is a Greek New Testament.
Anyway, out of this controversy came the Cooperative Baptist Fellowship, another organization allowing churches to join loosely for the purpose of missions and others. Whoever said something about missions, that is exactly the point of having a convention. This idea came about in the 1810's with a man named Luther Rice, a Baptist missionary who needed to raise money for missionaries in Burma and India. He came up with the idea of a convention, that would allow churches to pool their resources and participate together in fulfilling the Great Commission. Out of this came the SBC, and for the first 80 years of its existence, there were no creeds to teach by.
Well anyway, back to the question at hand: as I understand it, the SBCT aligns more with the SBC, and the BGCT aligns more with the CBF. Today, the SBC has a huge problem with the CBF, and recently threatened (and maybe did) to pull out of the Baptist World Alliance just because the CBF joined it. While it can be said there are doctrinal differences, the CBF actually doesn't have any official statements on doctrine -- no doctrinal confessions or creeds. This is not their point. Their mission is to be an organization to allow smaller churches to join and fulfill Christian duties that may be difficult to do on their own - mainly missions. I don't know much about the BGCT, but they do partner with the CBF for some things. They probably don't contribute much to the IMB, but that doesn't mean they don't give to missions.
Here's a link to a brief history of all that other stuff if you care. To be honest, alot of it is just really stupid, and there's just no way that all of the inner-turmoil within Baptists can be pleasing to God. And there is a lot more to it than what I've put, but this is a gist.
http://www.txbc.org/1994Journals/May%201994/May94CoChairParmer.htmAnd here's the interview with Pressler who finally admitted that much of what they were doing was aimed at political domination of Baptists (for a long time they denied they had such motives)
http://www.txbc.org/1998Journals/September%201998/Sept98AReview.htmAlot of Baptist churches today are aligned with one or the other, and many with both. My old church in Houston allows members to designate money to either organization. However, because of this the pastor is not allowed to speak at some engagements of the SBC. I know alot of this just sounds silly, but there are some people who are as Baptist as texasag73 is Catholic

, and they care very much about these things (I'm not really one, but I know some).
[This message has been edited by setsmachine (edited 4/21/2005 11:16a).]