The original Old Man Logan originally appeared in a story by Mike Millar and has a fate very different from the second version of the character.
In 2014, Charles Soule and Steve McNiven’s Death of Wolverine story left the main universe Wolverine encased in adamantium and presumed dead. Roughly a year later Jeff Lemire and Andrea Sorrentino’s Old Man Logan #1 brought the older alternate universe Wolverine to Earth-616 as a replacement for the now-dead Wolverine.
However, while this version of Logan is based on the character introduced in Mark Millar and Steve McNiven’s Wolverine #66, he is not the same as the original Old Man Logan of Earth-807128 and actually hails from Earth-21923. Though the two elder Logans share the same backstory as written by Millar, their stories split beginning in Brian Michael Bendis and Andrea Sorrentino’s Secret Wars tie-in series, Old Man Logan.
Beginning in Mark Millar and Steve McNiven’s afformenti0ned Wolverine #66, the ‘Old Man Logan’ arc follows an aged Logan living in a dilapidated part of America dubbed the Wastelands. Logan no longer operates under the ‘Wolverine’ moniker since killing the X-Men while under the influence of Mysterio’s illusions. This event occurred when this Earth’s villains finally worked together and defeated a majority of Earth’s heroes, leading to the Red Skull’s rule of America and Maestro’s rule of the Wastelands with the help of his inbred Hulk family. After the death of Logan’s wife and children at the hands of the Hulk family, Logan finally pops his claws and sets out on a journey to kill Red Skull, and then kill the aged, evil Hulk. At the conclusion of the story, Logan takes Maestro’s youngest son, Bruce Banner Jr., under his wing in hopes of stopping him from becoming evil like his father.
This is where the two stories begin to differ, as the Wasteland is recreated on Battleworld with the new version of Old Man Logan before making his way to Earth-616 after the conclusion of Secret Wars. While on Earth-616 Old Man Logan joins the X-Men as a pseudo replacement for the now deceased Wolverine. In addition to helping the X-Men, he also prevents the events that led to the heroes fall in his world and stops an alt-universe Hulk family from nuking the world to bring about their rule. Eventually, Old Man Logan’s healing factor becomes near useless and he makes his way back to his original timeline to assist Danielle Cage in raising Hulk Jr. before he finally dies in Ed Brisson and Mike Henderson’s Dead Man Logan #12.