Twain actually wrote multiple versions, each unfinished, but all included Satan as a character. One version, The Chronicle of Young Satan, is about the nephew of Satan who lives in an Austrian village in the Middle Ages.

Another version, Schoolhouse Hill, has Huckleberry Finn and Tom Sawyer involved with Satan, who is referred to as "No. 44". It takes place in America.

The third version is called No. 44, The Mysterious Stranger, taking place in the Middle Ages as the first version did. This version introduces the duality of a person, the "Waking Self" and the "Dream Self".  It has an ending whereas the other two are unfinished.

Paine had possession of Twain's unfinished works after his death and added an ending he thought Twain had intended. After his death, the manuscripts were released to the public and critics found Paine had chosen the ending from a different version of the story and changed some of Twain's wording. The edition to which you are referring is called the scholarly edition, considered to be what Twain would have published if he had lived.