A nurse administrator mainly deals with administrative and managerial roles of the nursing profession, along with managing HR, finance, and health policies. A nurse anesthesiologist is a different field altogether. It involves preparing and administering anesthesia during surgeries and medical emergencies. To qualify as the director of a hospital, the first step is to get an MS in healthcare administration, which is different from MS in nursing administration. A hospital director is directly involved with the day-to-day running of the medical center, and has to oversee everything from finance, hospital personnel, public relations, and patient services. I would recommend you go through Stevens-Henager student reviews – the college offers an MS in both, nursing administration and healthcare administration. Study the course content so you get a clearer picture of what the programs are all about, and then make your decision.