For any aircraft or bird with wings, lift is produced by creating a greater pressure under the wing than above it. The wing surface must be either cambered (curved) or tilted to the air flow direction. Usually a combination of curve and camber is used.
The pressure difference is not created by differences in air speed above and below the wing, or because the air has 'further' to travel over the upper surface of a cambered wing. Any shape will produce lift if inclined or cambered (the main factor is drag). Classical theory of fluid dynamics does not predict lift (the correct equations (Navier Stokes Equations) are complex and until the computer were of small practical use).
Lift depends on the viscosity of air causing asymmetric flow. The effect is only apparent in a very thin layer of air adjacent to the surface of the wing at most a few cm thick, the boundary layer.
There are two types of flow in the boundary layer. Around the leading edge the air flows smoothly and behaves like a stack of sheets (laminae) sliding over each other - laminar flow. Further along the wing there is a transition to a turbulent flow. The laminar layer produces less drag, but the turbulent layer is less likely to move away from the surface. As flow speed increases the boundary layer starts to separate at the trailing edge of the wing and a vortex begins to form, moves back and then leaves the surface. This is the starting vortex which disrupts the symmetry of the air flow, causing differences in flow pressure and speed between the upper and lower surfaces of the wing - Lift. The vortex extends in a closed circuit of two real vortices trailing from near the wing tips (wing-bound vortex) and the starting vortex, forming a horseshoe shape and sometimes called the horseshoe vortex system.