Wind turbines and driven propellers are the same thing. In a wind turbine, the wind produces the relative motion between the wind and blades. In an airplane or ship, the engine spinning the propeller produces the relative motion between the air/water and blades. As far as the propeller is concerned, it doesn't care. There's relative motion between itself and the surrounding fluid. In a wind turbine the "lift" (it's not really called lift here as far as I know, but it is the component of the aerodynamic force that does what we want) is in the direction tangential to the blade rotation which causes the blades to turn, and does so more efficiently than if you relied on drag (i.e. the wind directly shoving the blades). In an driven propeller, the lift is the component of the aerodynamic force that points parallel to the axis of rotation (or perpendicular to the plane of rotation) which is forward in an airplane/ship propeller, or up in a helicopter rotor.
As for the momentum thing, I think it is enough but it is not very helpful on its own since all it is doing is taking the end product from the propeller, no longer caring about any physical characteristics of the propeller or conditions which it is operating under, and converting the result to another physical quantity (speed or movement). It's not useful in designing a propeller or predicting its performance.
It's like saying that all you need to predict a car's speed is the wheel radius and how fast the wheels are turning. Not untrue, but not very helpful. It'd be a lot better if you could describe the operation of the engine and the transmission transferring power to the wheels. Then you can design a car and predict its performance.