booster rocket vs takeoff booster

booster rocket and takeoff booster both are nouns.

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

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

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

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

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