box office vs ticket office

box office and ticket office both are nouns.

Word	Noun	Adjective	Verb	Adverb
box office	Yes	No	No	No
ticket office	Yes	No	No	No

As nouns, box office and ticket office are synonyms defined as:

box office and ticket office: the office where tickets of admission are sold

Other synonyms of box office include ticket booth.

box office (noun)	ticket office (noun)
the office where tickets of admission are sold	the office where tickets of admission are sold
total admission receipts for an entertainment