Question

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

Answer 1

The terms under which the states of the South could rejoin the Union provoked disagreement between those wanting to be more lenient and the "radical Republicans" who wanted to impose harsh terms.  Prior to his assassination, President Lincoln had proposed a "10 percent plan."  According to Lincoln's plan, as soon as 10% of a states voters would take an oath of loyalty to the Union, and the state adopted a new constitution banning slavery, they could be admitted back into the Union.  The radical Republicans wanted the majority of a states voters to take an oath of loyalty, as well as banning those who had fought for the Confederacy from participating in conventions to draft new constitutions and from holding pulbic office.