advertising agency vs ad agency

advertising agency and ad agency both are nouns.

Word	Noun	Adjective	Verb	Adverb
advertising agency	Yes	No	No	No
ad agency	Yes	No	No	No

As nouns, advertising agency and ad agency are synonyms defined as:

advertising agency and ad agency: an agency that designs advertisement to call public attention to its clients

advertising agency (noun)	ad agency (noun)
an agency that designs advertisement to call public attention to its clients	an agency that designs advertisement to call public attention to its clients