Lift is a consequence of different pressure, but that is a consequence of changing direction in the fluid. Difference in fluid velocity comes from changing direction. Lift comes from momentum transfer from the lifting body to the fluid, where the fluid's vector leaving the lifting body is redirected normal to it's vector encountering the lifting body. The reaction force is lift.
Consider the bottom of a planing hull. The water encountering the hull is redirected downward, and slightly forward in the direction of travel. There is no circulation.
Not to say that circulation isn't real. Of course it's real, and when it is fully established, after about 7 chords of travel by the foil in a steady state system, the resultant forces on the foil are much higher lift and lower drag than if circulation were not established. The conceptual error is in thinking that circulation is the reason for lift. And even that isn't a problem if you never have to think outside the box. But a fully cavitating prop, a surface piercing prop, a planing hull bottom, a supersonic wing, all make plenty of lift without circulation.