ad agency vs advertising agency

ad agency and advertising agency both are nouns.

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

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

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

ad agency (noun)	advertising 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