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Here's an analogy that helps me.
Imagine a rubber ball thrown against a wall. The ball exerts a force on the wall, for a time, during its collision. Why?
A) The ball deforms when it is in contact with the wall, causing pressure to be applied to the wall by the rubber where it is in contact.
B) The momentum of the ball changes between the time it is moving towards the wall and the time it is moving away. Therefore there must be an impulse applied to the ball and consequently a force applied both by the ball to the wall and the wall to the ball.
Which explanation is "correct"? Well they both are correct. They're just models at different scales. If you were able to make appropriate measurements of deformation of the ball, you'd find the total impulse applied to be consistent with the change in momentum.
The lift models are a little like that. You can look at the pressure acting on the surface of the wing at every point, a bit like A. Or you can look at the momentum change of the air that has been turned by the wing, a bit like B. The lift predicted by either model will be the same. The only difference is in the practicality of the calculation. In the case of the rubber ball, it's obviously simpler to measure the velocity before and after and calculate the impulse that way. With wings, it tends to be easier to look at the pressure distribution on the wing than to calculate the momentum change of every relevant element of airflow. Hence aerodynamicists tend to think of lift as being "caused" by the pressure distribution, which is in turn "caused" by velocity differences in the airflow around the wing.
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