Abraham Lincoln's two inaugural speeches differ in many ways. His first speech was aimed at urging the southern states not to secede, while his second dealt with what to do with them after the war's end. His position on slavery also differs between the two, with him downplaying the idea of emancipation in the first and defending it in the second. This being said, there are notable similarities between the two speeches.
In both inaugural speeches, Lincoln highlights the common bonds between all the states and speaks to the need to reestablish peaceful relations. In his first speech, Lincoln says that
We are not enemies, but friends. We must not be enemies. Though passion may have strained, it must not break our bonds of affection.
Compare this with his second inaugural address, in which he calls for peace "With malice toward none, with charity for all." These speeches show how Lincoln was committed to maintaining a strong union built on good relations between the states. He seems to be saying that the nation can work through its differences and stay united as long as both sides work together in good faith.
There is an idealistic tone to both these speeches. At the time of the first speech, there was a serious threat of bloodshed and war. By the time of the second speech, much American blood had already been shed. However, Lincoln is looking to "bind up the nation's wounds." In both instances, he seems to express his devout belief that the nation can come back together, despite seemingly irreconcilable differences.