Final answer:
The communication management between a nursing facility and the public is known as Public Relations (PR), which differs from marketing, box office management, and house management.
Step-by-step explanation:
The management of communications between the nursing facility and the public is called Public Relations (PR). The role of PR is to promote and protect the image of a healthcare facility in the eyes of the public. This could involve handling media inquiries, issuing press releases, and organizing public events to enhance the reputation and public image of the facility. While PR focuses on the facility's relationship with the public and media, other departments like the marketing office may be more concerned with strategizing advertisements for the facility. In contrast, the box office manager would handle ticket sales for an event, and the house manager and ushers would be responsible for managing the venue and audience during productions. Therefore, the correct answer to the question is Public Relations.