I did wonder about the story there myself. It’s not like there’s any law against a Conservative shul being called “Temple whatever”, nor against a Reform one being called “Congregation whatever”. I’m guessing here, since I don’t know any more about the synagogues in question than what I posted, but I suspect that Temple Beth El, the Conservative shul, is the older of the two and was originally Reform, and that it moved toward Conservative practice over the years, and eventually re-aligned itself with the Conservative movement.
The practice of calling Reform places of worship “Temple whatever” arose from a point of doctrine in the Reform movement, namely that at least in its early days it de-emphasized rebuilding “The Temple” in Jerusalem and held that all Jewish places of worship should be the equivalent, for Modern Jews, of the original Temple.
Most of the Jews who settled in the American South in the 19th century were Reform Jews from Germany, and so most of the oldest shuls around are (or were, historically) Reform (I’m leaving out coastal areas such as Charleston, Savannah, etc., where the oldest synagogues are generally Sephardic, having been founded in the 18th century by British or Dutch Jews of Spanish descent). Such is certainly the case with The Temple, the oldest and largest Reform congregation here in Atlanta. The Orthodox shuls came later, with the later waves of immigration (primarily from Eastern Europe, where the Reform movement was never dominant). The Conservative movement was a reaction to what its members considered the excessive liberalization of practice and observance of the Reform movement, and generally was the last to establish itself in most communities. A fair number of Conservative congregations were founded as Reform or Orthodox institutions, and changed as the demographics and beliefs of their membership changed. For example, Atlanta’s Ahavath Achim was founded in 1887 by Eastern European Jews who presumably were not comfortable with the Reform orientation of The Temple; its ritual and practices at the time would be considered Orthodox today. By the middle of the twentieth century, however, Ahavath Achim had aligned itself with the Conservative movement. Along the way, Ahavath Achim has spawned several other congregations as members whose beliefs and practices led them in different directions (including Congregation Beth Jacob, now Atlanta’s largest Orthodox congregation).
This process of changing affiliation as the membership changes continues today, FWIW. Just recently, another long-standing Atlanta congregation, Shearith Israel, which was founded by Eastern European Jews in the early twentieth century and had long been associated with the Traditional movement (a sort of middle ground between the Orthodox and Conservative movements), voted to realign itself with the Conservative movement, leading the rabbi and a group of members to split off and found a new Traditional congregation.
By the way, Aries28, there’s an overview of what synagogues are like, with a section on visiting synagogues for non-Jews, at http://www.jewfaq.org/shul.htm .
And it turns out, I’m wrong after all that. Temple Beth El has a history of the Jewish community in Birmingham page on their web site.