ELI5 Aircraft Engines - why propellers on military planes vs jet engines?

ELI5 Explain Like I'm 5: Bite sized answers to stuff you should know about - in a mini podcast

Why do military planes like the Hercules C-130 and Airbus A400M military transport planes use propellers instead of jet engines? What makes them more versatile for shorter runways? Why is a turboprop engine not the same as regular piston propeller engines? Explain the difference between a turbojet, turbofan and turboprop.

... we explain like I'm five

Thank you to the r/explainlikeimfive community and in particular the following users whose questions and comments formed the basis of this discussion: elena1995x, dirschau, airbornerodent, frat_guy_pa, arztnur, noxious89123 and kaiisim

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