With aerodynamics as a physics subject I only spend my leisure time on I would put it this way:</p>

Air have some basic properties, when it comes to model aeroplane lift, mass, densinity and viscosity is the important ones.
With the wing creating lift some observations can be done and math formulas formulated to explain these observations.</p>

Lift is proportional with angle of attack until the wing stall. The AoA-Lift slope is straight a certain AoA range. Makes lift=AoA</p>

If pressure is measured under and above the wing a pressure difference is measured. Multiplying wing area with average pressure difference the total lift is found.</p>

Makes lift=area*pressure difference</p>

Using the Bernoulli theorem, the speed differences between air passing under and over the wing can be found (calculated). Or if the speed is known, the pressure and hence lift found. Fits nice with the above expression, lift=area*pressure difference</p>

Observing a wing in a wind tunnel with smoke markers, the air passing over the wing is observed to "speed up". In real life the air is stationary and the wing passes by. Thinking about it the air "rotates" around the wing, and there you have the idea of the rotation math. The math is then an abstraction used to explain lift.</p>

As I see it, none of the above is mutually exclusive. It's different ways to explain the observations.</p>