The difference being that Mr. Lincoln believed every man had the unalienable right of owning himself, and Mr. Stephens believed every white man had the unalienable right to own black men.
Looking at all the public pronouncements of both men makes it perfectly clear that there was an enormous difference between them on the issue. Cherry-picking particular statements can obscure this, if your goal is to do so.
A great many men who were opposed to slavery in the 1850s had great doubts as to whether blacks could ever be succesfully incorporated into American society. Since we are still struggling with the issue 150 years later, their doubts are quite understandable.
Then Mr. Lincoln's political ambitions apparently outweighed his principles, inasmuch as he was perfectly willing, in March of 1861, to endorse an amendment to the United States Constitution that would have permanently legalized slavery by preventing Congress from ever interfering with its practice.