loyalist vs booster

loyalist and booster both are nouns.

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

As nouns, booster is a hypernym of loyalist; that is, booster is a word with a broader meaning than loyalist:

loyalist: a person who is loyal to their allegiance (especially in times of revolt)
booster: a person who backs a politician or a team etc.

Other hypernyms of loyalist include admirer, champion, friend, protagonist, supporter.

loyalist (noun)	booster (noun)
a person who is loyal to their allegiance (especially in times of revolt)	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.