prompter's box vs booth

prompter's box and booth both are nouns.

Word	Noun	Adjective	Verb	Adverb
prompter's box	Yes	No	No	No
booth	Yes	No	No	No

As nouns, booth is a hypernym of prompter's box; that is, booth is a word with a broader meaning than prompter's box:

prompter's box: a booth projecting above the floor in the front of a stage where the prompter sits; opens toward the performers on stage
booth: small area set off by walls for special use

Other hypernyms of prompter's box include cubicle, kiosk, stall.

prompter's box (noun)	booth (noun)
a booth projecting above the floor in the front of a stage where the prompter sits; opens toward the performers on stage	small area set off by walls for special use
	a small shop at a fair; for selling goods or entertainment
	a table (in a restaurant or bar) surrounded by two high-backed benches