First, it should be made clear that Lincoln's views on slavery as a political issue changed over the course of the war. But before the war, Lincoln argued that slavery should not be allowed to expand in to western territories. He did not claim, nor did he believe, that slavery...
could be abolished in the South, where it already existed. In fact, there was talk in the immediate aftermath of secession of enticing southern states back in the Union by passing a constitutional amendment that guaranteed protection for slavery in the South. Over the course of the war, his views changed, even though it is significant that the Emancipation Proclamation, which in any case freed only a handful of slaves, was framed as a wartime measure.
Frederick Douglass, on the other hand, was an abolitionist, and argued that the Constitution represented a Faustian bargain because of its protections for slavery:
The parties that made the Constitution, aimed to cheat and defraud the slave, who was no himself a party to the compact or agreement. It was entered into understandingly on both sides. They both designed to purchase their freedom and safety at the expense of the imbruted slave. The North are willing to become the body guards of slavery — suppressing insurrection — returning fugitive slaves to bondage — importing slaves for twenty years, and as much longer as the Congress should see fit to leave it unprohibited, and virtually to give slaveholders three votes for ever five slaves they could plunder from Africa, and all this to form a Union by which to repel invasion, and otherwise promoted their interest.
He pushed for immediate and complete abolition of slavery, which he claimed should be followed by full political rights. He welcomed the onset of the Civil War and recognized it immediately, unlike Lincoln, as an opportunity to destroy slavery. He argued for an Emancipation Proclamation and for the right of black men to serve in the Union Army. In short, Lincoln felt constrained by the Constitution not to abolish slavery, while Douglass wanted immediate abolition .