The nickname "Unconditional Surrender" was given to Grant not after the surrender of Robert E. Lee at Appomattox, but after the much earlier surrender of Fort Donelson on the Mississippi in 1862. Although Grant used the words "unconditional surrender" in his correspondence with Simon Bolivar Buckner, the surrendering Confederate general who happened to be an old friend from West Point, after the surrender Grant actually treated the captured confederates well, paroling them rather than imprisoning them. The press played up the coincidence of "Unconditional Surrender" with his initials.
Three years later, when he accepted the surrender of Robert E. Lee, the terms were notable for their generosity. "Magnanimous" was the word frequently used to describe them at the time. Following the general principles set out by Abraham Lincoln, Grant's terms were that there would be no reprisals, and that every soldier was free to go home and abide by the laws of his state. In addition, he gave the starving Confederates rations and allowed them to keep their horses. This was very well received by Lee and the Confederate army.