takeoff rocket vs rocket engine

takeoff rocket and rocket engine both are nouns.

Word	Noun	Adjective	Verb	Adverb
takeoff rocket	Yes	No	No	No
rocket engine	Yes	No	No	No

As nouns, rocket engine is a hypernym of takeoff rocket; that is, rocket engine is a word with a broader meaning than takeoff rocket:

takeoff rocket: the first stage of a multistage rocket
rocket engine: a jet engine containing its own propellant and driven by reaction propulsion

Other hypernyms of takeoff rocket include rocket.

takeoff rocket (noun)	rocket engine (noun)
the first stage of a multistage rocket	a jet engine containing its own propellant and driven by reaction propulsion