GOP: Godly Orthodox Party
"Orthodox" means "right-teaching" and within the context of the GOP refers to the right-wing base of the larger Republican Party which is as a whole more conservative than orthodox. The right-wing base includes the whole "religious right", but is made up mainly of the "Christian right". Many people mistakely believe the Republican Party and the GOP are the same and on many levels it does appear that way since it can often be difficult to understand the constant flux of political alliances and postering within the parties, but the Republican Party is the larger "umbrella" party which covers many of the looser coalitions which are often only active during election years.
I registered as a Republican to reach out to more allies, but I'm actually with the GOP.