Titles are funny - they can mean whatever the person assigning them means. In a small company, you may have a lot of "vice presidents" to help people feel good about their jobs if there isn't a lot of pay. Sort of silly if you ask me. But anyway...

Usually a manager is simply in charge of people or a project (or both). Usually, a director is higher than a manager. Also, non-profit organizations are usually headed by a director, in which case, it's a higher-level position than the title would indicate.

Administrator can mean a lot of things too. Some towns will have a town administrator, which is like what people think of as a mayor, but the administrator actually does the work.

In a typical (American) company, you may have people who report to supervisors, who report to managers, who report to directors, who report to vice presidents, who report to the president. Sometimes there are senior vice presidents between the VPs and the president. Sometimes there are senior managers who are between the managers and the directors. Sometimes "professional" or "white collar" employees will report directly to a manager, and there are no supervisors. It just depends.