Turbojet compresses air to then ignite it and get thrust out of the exiting expanded gas.
Turboprop uses that gas to spin a secondary turbine, that is geared to drive a propeller.
Turbojets are faster overall when cruising, can fly higher, And don’t have the complexity of a gearbox added to it.
Modern airliners use Turbofans, where the passive turbine is used to spin a ducted fan. The ducted fan produces thrust more efficiently than propellers, and the cool air it blows is used around the engine to keep it cool, increasing efficiency as well. In most airliners, the fan part actually produces most of the total thrust over the turbojet.
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