prompt box vs prompter's box

prompt box and prompter's box both are nouns.

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

As nouns, prompt box and prompter's box are synonyms defined as:

prompt box and 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

prompt box (noun)	prompter's box (noun)
a booth projecting above the floor in the front of a stage where the prompter sits; opens toward the performers on stage	a booth projecting above the floor in the front of a stage where the prompter sits; opens toward the performers on stage