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In the context of producing a pulling force perpendicular to the 'spinning plane' of a propeller/fan,
is it correct to say that a propeller mainly achieves it's force by being aerofoils producing lift and a fan mainly achieves it's force by utilizing Newtons third law?

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There is no difference in physics between a propeller and fan. In English the distinction is probably that a fan moves air while the propeller moves the vehicle through the stationary air (or water).
edit: Although aerospace engineers call the front stage of a turbine engine a "fan".

There is a difference between an aerodynamic regime at low speeds and higher pressures where the air behaves as a fluid, and low pressure regimes where it is purely mechanical 'billard balls' hitting flat blades - as in a high vacuum turbo molecular pump

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Actually, there ARE some differences. You would not like to be in the wake of a propeller, if all you want is gentle, whisper-quiet air movement. Ventilator fans, both cooling fans [i.e., automotive, refrigirators, etc.] are WAY gentler than propellers, or, jets...

Consider your desk-top ventilator and, say, a hair dryer or a leaf blower... you will NOT use a hair drier to cool in a hot summer, right? The same with airplane props. It all revolves around the issue of what flow rate is needed in a given diameter of the device. The more flow that needs to be "squeezed" through a given diameter, the more mayham it creates. Not something that you will welcome in your room...

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Main difference is the pressure differential between up-flow side and down-flow side of the "disk". The "disk" is the virtual circle defined by the rorating blades. In oropulsive devices, such as airplane and helicopter rotors and turbofan engines, this pressure difference, also known as "disk loading", is MUCH higher in propulsive devices than in air-moving devices.