Just saw the Deadpool movie (amazing movie). Before watching this movie, I was sure he would have the same abilities as Weapon XI (from X-Men Origins: Wolverine).
Stryker activates a mouth-sewn Wade, now known as Weapon XI, a "mutant killer" with the powers of multiple mutants, who he refers to as the "Deadpool."
Why is this Deadpool totally different from Weapon XI (no adamantium claws, no energy beam from eyes)?
The new Deadpool exists in the timeline created after X-Men: Days of Future Past (which Deadpool himself is fully aware of, and jokes about). The actual implications of the time change are not fully understood, but clearly resulted in a totally different origin story for Wade Wilson.
For example, Wade was born a mutant and recruited by Stryker according to Wolverine Origins. This was not the case in the new Deadpool movie. In this new reality, Wade was basically a human with hints of underlying mutant DNA, which Francis' experiments were designed to bring to the surface. In addition, it doesn't look likely that Wade and Stryker ever met. How these differences came to be? Who knows - it's probably an unexplainable butterfly effect from a most insignificant detail that ultimately changed the world.
