placement office vs placement center

placement office and placement center both are nouns.

Word	Noun	Adjective	Verb	Adverb
placement office	Yes	No	No	No
placement center	Yes	No	No	No

As nouns, placement office and placement center are synonyms defined as:

placement office and placement center: an office that finds suitable employment for applicants

placement office (noun)	placement center (noun)
an office that finds suitable employment for applicants	an office that finds suitable employment for applicants