how does president Lincoln frame the causes of the war in a different way than how a radical northerner or confederate sympathizer would?

By following the model of his "Gettysburg Address" in his speech, President Lincoln frame the causes of the war in a different way.

Explanation:

"Lincoln" decided to deliver a speech to the people where he used his model of Gettysburg Address in his speech rather than detailing his plans for Reconstruction in his Second Inaugural Address. He rejected the Radical Republicans' triumphalism in Congress, who had a desire to rule over the Southern States which was defeated, with malice. Lincoln persuaded the audience with "malice towards none, with charity for all" by spurring the Confederate President Jefferson Davis who urged the Southerners "to stand to our arms". He did all of the things mentioned in his speech after abolishing slavery from the States.