The main difference between the First and Second Inaugural Address of Abraham Lincoln was the different contexts in which they were given. In the First Inaugural, Lincoln was in a precarious position. He had received less than 40 percent of the popular vote, and the nation was divided, with 7 states having seceded and the country on the verge of civil war. In this context, Lincoln's focus was not so much on slavery per se, but on national unity and the mandates of the Constitution with respect to the relationship of state and federal governments. The tone of the address is legalistic, focused on specific details of the rule of law, including reassuring southerners that he did not see the Constitution as justifying federal interference in internal arrangements of the Southern states (i.e. slavery) and that he would enforce the Fugitive Slave Act. Although Lincoln was personally opposed to slavery, he saw his position as President as committed above all to the enforcement of the rule of law and his priority as national unity.
In his Second Inaugural Address, the North had almost won the Civil War, and Lincoln's concerns were quite different. No longer needing to accept slavery as the price of national unity, he was focused on making the wartime Emancipation Proclamation the grounds of permanent abolition of slavery. His next major concern was reconciliation, as exemplified in his phrase "with malice toward none; with charity for all." His second speech is much less legalistic and contains fewer specific details, but has a more idealistic moral tone.