Both Mr. Micklethwait and Mr. Smith were told they were in charge. And both report directly to Mr. Bloomberg, who was forced to negotiate a tentative peace between them.

Mr. Bloomberg, Mr. Smith and Mr. Micklethwait declined to comment.

A major issue, the people said, is that Bloomberg, as a media organization, is struggling to determine exactly what it wants to be. Mr. Bloomberg has a personal fortune of around $36 billion, and the company employs some of the most talented journalists available — it won its first Pulitzer Prize this year. On some days, the people said, he seems bullish about the media company. On others, he seems to see it as a threat to the terminal business, to be managed accordingly.

What seems clear to many, and what has been outlined in general terms, is a retrenchment, away from the sprawling media organization that Mr. Smith was tasked with building, and toward one that focuses on subjects most important to the wealthy corporate readers that make up most of its customer base. Mr. Bloomberg and Mr. Micklethwait have signed off on a new editorial project, focused on providing nuanced and timely content, which is hiring several new writers, according to a person briefed on the plans.

At a town hall meeting shortly after he arrived, Mr. Micklethwait laid out some of his editorial vision. He told staff members that he wanted to own the company’s “home territory.” That, he said, is “some version of business, finance, markets, technology — and then also what I think of as power.” Those topics, he said, are “of great interest to many of the people who buy terminals.”

Mr. Bloomberg has already turned a critical eye to the company’s money-losing television operation, where he surprised some of the staff who did not expect the founder and chief executive of a company to provide detailed input on seemingly minute matters.