Why are airplane propellers shaped differently from boat propellers or fan blades?
I asked that question near the end of this thread.
Simple answer: Because air and water behave very differently, and airplane propellors, boat propellors, and fan blades operate at very different speeds.
All of them use a shape which causes the air or water to move at (ideally) right angles to the direction of the propellor. The wider boat propeller blades and fan blades work better because of the lower speed than narrower airplane propellors. Boat propellors have a different profile because water is an incompressible fluid and behaves very differently than air.