Wade Wilson was GIVEN the ability to regenerate by the Weapon X program, and later took the moniker of Deadpool. In "Wolverine," Wilson apparently has super-speed or something.

Then later in the movie, Stryker unveils "Weapon XI," a genetically-engineered mutant with Cyclops' eyes, Sabretooth/Wolverine's regenerative abilities, and adamantium katana swords that come out of his wrists. Stryker calls this thing "Deadpool." Oh, and it also has no mouth. Wolverine recognizes Weapon XI/"Deadpool" as Wade Wilson, even remarking "Someone finally shut you up" or something to that effect whilst fighting him.

And no, Wade never breaks the fourth wall (sadly). But Reynolds was damn good casting for him ... too bad they ruined it.

Oh, and C3PX, here's my favorite example of Deadpool's fourth-wall-breaking in the comics: