Same gas generator core, three completely different ways of turning that core's power into thrust — and the split all comes down to one number: bypass ratio.
All three engine types share the same fundamental core: a compressor raises intake air pressure, fuel is burned in the combustor, and a turbine extracts just enough energy from the hot gas to keep driving that compressor. What each design does with the leftover energy is what makes it a turbojet, a turbofan, or a turboprop. A turbojet sends essentially all of it out the back through a single exhaust nozzle as high-velocity jet thrust. A turbofan uses an extra turbine stage to drive a large ducted fan, splitting the airflow into a fast "core" stream and a much larger, slower "bypass" stream around the outside. A turboprop takes that idea further, using nearly all of the core's spare power to spin an external propeller through a reduction gearbox, with only a small residual jet contribution. The single number engineers use to describe where an engine sits on this spectrum is the bypass ratio — the mass of air that goes around the core divided by the mass that goes through it.