Yeah, the movable vs. immovable distinction is the big difference here. If it's a truly immovable wall, then the ground exerts a great backward force to keep the wall in place during the collision, which the wall transfers into the car.

But if the car just busts straight through a wall of equal mass (and a comparable crumple zone), then it will be just like the car/car case energetically: the car and wall both continue at 50 mph following the collision.