Urr.. right. Except that:
- The southern states had full representation in the national government, whereas the colonies had very little
- The people in the south got to vote for their national leader, whereas the colonies' leader was given to them through heredity
- The people in the south got to vote for their own state governments and governors, whereas colonial governments were fully or partially installed by the national government
- The colonists were instituting an entirely different form of government, whereas the confederacy was pretty much just trying to protect the right to own slaves
- In the three decades prior to the civil war, the southern-allied Democratic party controlled the House of Representatives for 18 of those years, the Senate for 24 of those years, and the Presidency for 18 of those years, whereas in the 30 years prior to the American Revolution, the American colonists had little to no say in British national politics
Aside from all that, though, yeah... they're very similar.