[This happened, but Wolverine doesn't remember: The events of X-Men (2000) and any alluded to previous events, through his departure from Xavier's School for Alkalai Lake. He arrives at Alkalai Lake and finds it apparently deserted. He is captured by the military research team that has been secretly working there since the place had been shut down nearly fifteen years ago. Stryker is still in charge and working on additional experiments and more than ecstatic that his 'pet project' has 'come home'.]
This is what he does remember: Wolverine has been at Alkalai Lake for the last several years - he's not sure how many; he's not sure of much at all. All memories of anything prior to his waking at Alkalai Lake after his capture have been erased or blacked-out and are inaccessible. He remembers nothing of the X-men or how he got back to Alkalai Lake. He does remember his previous time at Alkalai Lake when the initial experiments were performed and he remembers that escape, then there is blackness and he remembers waking up inside the facility again.
He's tired of the experiments, the trials, the tests... all of it. He's been plotting and planning and, finally, one day, makes his escape attempt...
...only to end up in Milliways.
Key Differences: Wolverine has control issues with the Adamantium claws surgically implanted in his forearms - they tend to extend on their own when he experiences extreme emotions: anger, fear, lust, etc. This is more of a problem as he is easily spooked and reacts badly to stressful situations. He's not necessarily overly violent, just extremely defensive.
Wolverine is the property of Marvel Comics and 20th Century Fox, as he is based on the movie-version, with a few tidbits from various comics thrown in for background hole filling. Wolverine is being used for play at otherways, no copyright infringement intended. Wolverine is portrayed here by Hugh Jackman.