Is Hulk in The Avengers the same Hulk from The Incredible Hulk?

The Hulk from The Avengers was intended to be a continuation of The Hulk from The Incredible Hulk. Due to a(n) (overblown) dispute between Edward Norton and Marvel Studios on the changes Norton made to the script, which were filmed and then cut by the studio, Norton was not asked to reprise his role. Norton's press release at the time of the film release was as follows:

“Like so many people I’ve loved the story of The Hulk since I was a kid, so it was thrilling when Marvel asked me to write and help produce an altogether new screen incarnation, as well as play Bruce Banner. I grew up reading Marvel Comics and always loved the mythic dimension and contemporary themes in the stories, and I’m proud of the script I wrote. In every phase of production, including the editing, working with Louis Leterrier has been wonderful…I’ve never had a better partner, and the collaboration with all the rest of the creative team has been terrific. Every good movie gets forged through collaboration, and different ideas among people who are all committed and respect the validity of each other’s opinions is the heart of filmmaking. Regrettably, our healthy process, which is and should be a private matter, was misrepresented publicly as a ‘dispute,’ seized on by people looking for a good story, and has been distorted to such a degree that it risks distracting from the film itself, which Marvel, Universal and I refuse to let happen. It has always been my firm conviction that films should speak for themselves and that knowing too much about how they are made diminishes the magic of watching them. All of us believe The Incredible Hulk will excite old fans and create new ones and be a huge hit…our focus has always been to deliver the Hulk that people have been waiting for and keep the worldwide love affair with the big green guy going strong.”