booster vs booster rocket

booster and booster rocket both are nouns.

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

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

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

booster (noun)	booster rocket (noun)
an additional dose that makes sure the first dose was effective	the first stage of a multistage rocket
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.