In the November 19, 1863 Gettysburg Address, President Lincoln understands freedom as a task yet to be completed. The Founding Fathers had started it ("Fourscore and seven years ago our fathers brought forth, on this continent, a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal"), many have died in the Civil War to finish it, and the best way to honor those who has given their life to such an elevated cause is to complete it by the ones still alive. Otherwise, the nation would die.
On the other hand, in Letter from a Birmingham Jail, Luther Martin King states that "freedom is never voluntarily given by the oppressor; it must be demanded by the oppressed". As the thirteen colonies have done in the past, the oppressed of today must fight for their God given right of freedom, because the privileged never give up their privileges willingly, they would stop being so.
Something that tells them apart is that Lincoln had to believe in fighting for freedom through a war (he was left with no other choice). Martin Luther King advocates for nonviolent direct actions.
