ticket office vs box office

ticket office and box office both are nouns.

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

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

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

Other synonyms of ticket office include ticket booth.

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