booster rocket vs booster

booster rocket and booster both are nouns.

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

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

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

booster rocket (noun)	booster (noun)
the first stage of a multistage rocket	an additional dose that makes sure the first dose was effective
	the first stage of a multistage rocket
	an amplifier for restoring the strength of a transmitted signal
	a thief who steals goods that are in a store
	someone who is an active supporter and advocate
	a person who backs a politician or a team etc.