If both propellers and wings are airfoils, then why do propellers deflect air perpendicularly to the rotor, but wings not? Here is my dilemma.  I have seen a lot of videos of airfoils in wind tunnels, and I've noticed how the airflow always moves away from the trailing edge parallel to the wing, or at a very small angle away from the wing as in this video: 
                
            
I've also heard that propellers are nothing more than rotating wings (airfoils), producing lift sideways as opposed to upwards.  What confuses me is that in the case of the propeller, the airflow leaves the propeller at a much higher angle, and not straight as is with the wing.  In other words, the airflow is deflected backwards from the prop.  I just can't understand how the wing and propeller, which are two very similar shapes (maybe not that similar, but they operate by the same principle), deflect air in two radically different directions.
I have a few thoughts on why this happens, but I think it's better if someone tells my first.
Don't let wind tunnels fool with your perception of reality. In the real world, it's the wing that moves while the air remains stationary.

Consider a video just like the one you posted, but filmed with a stationary camera. (The one in your video is attached to the wing and moves along with it.) You'd see the folowing scenes:


The field of view is filled with stationary air.
A wing quickly passes through the video from right to left.
The air now moves downward more or less vertically.