Both fans and propellers move a quantity of air. In the former, that is the end goal. In the latter, this movement of air creates a force in the direction opposite to the airflow. So, why are the blades so different from each other?
2 Answers
A fan designed for use in the home must be much quieter in operation than a fan that is designed for maximum propulsive efficiency. The quietest air-moving fans have blades with chord widths so large that the trailing edge of one blade is overlapped by the leading edge of the next blade. This causes more air drag losses but greatly reduces noise.
In addition, to suppress the formation of vortices at the trailing edge tip of a fan blade, the designer reverse-sweeps the blades so the leading edge of the blade tip is ahead of the leading edge of the blade root. This also makes the fan quieter.
The jet engines used in planes compress air to make static thrust. So the weird looking blades in jets are specially designed to compress air. On the other hand, fans at home are designed to make a simple air flow, hence the simple design.