fan-jet vs jet engine

fan-jet and jet engine both are nouns.

Word	Noun	Adjective	Verb	Adverb
fan-jet	Yes	No	No	No
jet engine	Yes	No	No	No

As nouns, jet engine is a hypernym of fan-jet; that is, jet engine is a word with a broader meaning than fan-jet:

fan-jet: a jet engine in which a fan driven by a turbine provides extra air to the burner and gives extra thrust
jet engine: a gas turbine produces a stream of hot gas that propels a jet plane by reaction propulsion

fan-jet (noun)	jet engine (noun)
a jet engine in which a fan driven by a turbine provides extra air to the burner and gives extra thrust	a gas turbine produces a stream of hot gas that propels a jet plane by reaction propulsion
an airplane propelled by a fanjet engine