The character that appears in that film is *not* Deadpool. Instead, it's Wade Wilson, a character who shares the same name but is a significantly different character.
In X-Men Origins: Wolverine, Wade Wilson is depicted as a former SAS soldier with a healing factor who is recruited by William Stryker to join his Weapon X program. He is given the code name "Deadpool" and is transformed into a brutal, masked assassin. This version of Wade Wilson is a far cry from the quippy, fourth-wall breaking antihero that we know and love from the comics and the later Deadpool movies.
The *real* Deadpool, the one we're familiar with, was not introduced until the 2016 film *Deadpool*, which was a more accurate adaptation of the character from the comics.