From a "pressure make plane go up" point of view, yeah I guess it's all the same, but I think the methods are distinct enough. Bernoulli's works by reducing pressure above the airfoil. Action reaction increases pressure below it.

they are directly linked and have to be equal.

I don't follow. Unless you're trying to account for the total amount of lift with each separately and the math lines up. I guess that wouldn't surprise me because bernoulli's principle is derived from newtonian physics, specifically the second law F=MA, and both contribute to the total production of lift, but not in equal amounts. Symmetrical airfoils for example rely more on angle of attack to generate lift, while an asymmetrical one can maintain level flight at a negative aoa at high enough airspeed.