The character of Wolverine in the movie ‘Logan’ is inspired by “Old Man Logan” story based on a dystopian future where the supervillain Mysterio finally prevailed over Wolverine. The story of Logan is set up in 2029 which is way past 2024, the year mentioned in the epilog scene of X-Men: Days of Future Past. In the movie, Prof. Charles Xavier is still alive and mutants much younger have fallen. In the comics, it’s the post-apocalyptic world dealing with the implications of generations of mutants wiped out by the deadly forces.
The plot of the movie revolves around Logan delivering young Laura/X-23 to the mutant sanctuary called Eden, and he is being consistently chased by the army of cyborgs led by Donald Pierce. In the comics, the Reavers are much deadlier and special instead of just another enhanced soldier.
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In the Marvel comics universe, in 2014, the title ‘The Death of Wolverine’ ended the character for good as Wolverine found himself encased in unbreakable adamantium rock, leaving X-23 (the Clone of Wolverine) as the new Wolverine for the Marvel universe.