They are all airfoils (or hydrofoils if we are talking about a ship propeller).
I have read lots of explanations about how aircraft fly, some better than others, some plain wrong; but I don’t remember (not that I have a great memory anyway) having read anyone where they explain that the concept of an airfoil is the same in all cases: an airfoil forces the air in a different direction (except in the case of some sails), thus creating a force.
In order to understand this, let’s think about how we swim. We basically push the water backwards in order to move forward. Or if we are in the bottom of the pool, we push the water down in order to go up. The air is a fluid, like the water, so we can move it. If we push air backwards, we move upwards too. But we need to push a lot of it to sustain ourselves.
Let’s use another example. You can try this at home. If you put the outer rounded part of a spoon under the flow of water, the water will “stick” to it as it flows down and by the time it leaves the spoon, it will have changed its direction, like this:
The flow of water changes its direction when it moves over the rounded surface. The same thing happens in an airfoil. (Image from http://www.terrycolon.com)
Now imagine the water flow is wind. If the wind travels through a sail with a similar shape it will end up being forced in a perpendicular direction, so the ship will move in t he opposite direction (as we do when we swim). A propeller does the same thing, when it moves through the air or water, it forces the fluid backwards. You can do the same thing with your hand in front of your face. Put your right hand in fron of it, with your palm facing 45º towards you (midway between left and backwards) and turn your elbow quickly to move your hand over your face. You will notice the air hitting your face. This is what a propeller does!
So as we can see the reason why airplanes fly is not such a mystery: when they travel through the air, the wing pushes some air down, in the same way as the spoon. In this case the force is called lift.
Wings have a profile that forces the air downwards. The air sticks to it as the water to the spoon. Since it forces the air down, it generates an upwards force, in the same way move up inside a pool when we push water down.
A F1 car wing does the opposite thing. It moves air up, thus pushing the car down and keeping it on the road.
An F1 rear wing, as we can intuitively see, moves the air up, thus creating downward force. (Image from grabcad.com)
So that’s basically it. This is of course a very simplified explanation, but I really think that you don’t need to talk about mathematical formulas and complicated physics to have a basic understanding of how aerodynamics work.
Hope that was useful for someone!