takeoff booster vs booster rocket

takeoff booster and booster rocket both are nouns.

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

As nouns, takeoff booster and booster rocket are synonyms defined as:

takeoff booster and booster rocket: the first stage of a multistage rocket

Other synonyms of takeoff booster include booster, booster unit, takeoff rocket.

takeoff booster (noun)	booster rocket (noun)
the first stage of a multistage rocket	the first stage of a multistage rocket