It would be great if there were absolultely hard and fast rules governing these kinds of language choices, but unfortunately there aren't. In the case of a journalist and the news organization that buys the journalist's coverage, I would say that it goes back to the relationship involved: if a journalist sells an occasional story to a newspaper, or shops around for the highest bidder on a story, I would call whoever buys the story a customer (which fits PanPan's definition). However, a journalist not directly employed by the newspaper but in a formal relationship as a stringer, say, covering events in a particular city, submits a story, I would call the newspaper a client, since the journalist is selling the story as part of an ongoing service to the newspaper. Chances are very good that there is an agreement between the parties that gives the newspaper some degree of exclusive rights to the journalist's stories and that gives the journalist some guarantee in regard to price, etc.
Nick