What was the nature of the disagreement about the terms under which former confederate states might rejoin the union after the civil war

The Confederates and Union had a disagreement regarding the legitimacy of the Confederacy and the abolition of the slave trade in the US. The Confederates is a group of states in the US that are known as slave states. The Confederacy was built with the notion of eliminating slavery in the US. The Union is a government in which supports slave trade in some of the states.