The fundamental difference was in how the states would be admitted back into the union. According to the Presidential reconstruction plan, 10% of people in those territories would have to support coming back into the union if they accepted emancipation of African-American people. The congressional plan claimed that when they seceded that they abandoned their claims to the United States constitution and that they should be governed regardless of whether or not they want to be governed by the northern congress.
There were divergent views because of their opinion on how the southerners should be handled. The view of many people such as the Radical Republicans wanted to punish the southerners as much as possible. People like Lincoln, and later Johnson, believed that this would be humiliating for them and further agitation was not necessary so they cut them some slack on numerous issues.
The Civil War occurred from the years of 1861 to 1865. If we are talking about the reelection in 1864, then it means there was only one year left in the Civil War. Therefore, the Civil War was close to ending.
