How does the 13th amendment differ from the emancipation proclamation?

The 13th amendment declared them as actual citizens. The emancipation proclamation supposably 'freed' the slaves but since it was still during the civil war the slaves in the south/confederacy were not free until the end of the war in 1865

Lincoln's Emancipation Proclamation occurred after the Battle of Gettysburg in 1863 and almost in the middle of the Civil War. Lincoln only declared the slaves of the Confederate occupied territories/States to be free. It may be considered similar to an executive order, but it had questionable legal and lasting effect.

The 13th Amendment abolished slavery permanently throughout the U. S. A. in December 1865 (after the end of the war) by legislative amendment of the Constitution. It was ratified by the States in haphazard fashion.