The client is the consumer in which an advertising company will target. they are a single member of their target audience, which they will try to entice and make want their product through the advertising process.
An ad agency is an outsider company who's specialist at advertising, and companies can hire them to advertise their product. this company is very similar to PR. The company will hire from the ad agency and pitch to them their product, target audience, and a primary marketing scheme. the ad agency will then build upon this with their specialist skills so to create a great advertising campaign which serves its purpose. The advantages of an ad agency over full timed hired employees, as it saves on wages and the company benefit from experts at advertising.