To add to what LemonThrower has said, generally, the shareholders of a public or private corporation elect a board of directors with overall supervision of the company, and the board of directors appoints corporate officers to implement the board’s resolutions and conduct the day-to-day operations of the corporation. Typically the board of directors has a chairman/woman, who may or may not be a corporate officer.
Generally, the board of directors has very few restrictions on what titles they can give corporate officers. Historically, the officers were president, vice president(s), secretary, treasurer (and sometimes with assistant secretaries and assistant treasurers). More recently, corporations gave a few descriptive job titles like chief executive officer, chief Financial Officer and (sometimes) chief operating officer, to designate the people that were in overal charge, in charge of finances and in charge of operations because that was often not clear (i.e. is the board chairman the chief executive in charge of everything, or only a director who heads board meetings).
In the last 10-20 years, descriptive job naming has expanded, with corporations having a chief [whatever] officer to head up the [whatever] function, where previously these officers would most likely have been the vice president for [whatever]. In addition, the title managing director has become common, particularly in financial companies, to denote someone above the Vice President level but below the Senior/Executive Vice President level (which is in contrast to the European naming scheme, where the MD is often the guy in charge of the whole shooting match).
The difference between someone who is a corporate officer and who is not has some legal distinctions (can he or she sign certain documents or accept legal process for the corporation), but few operational ones. Still, a good rule of thumb is if the person has one of the traditional titles in their corporate title (president, VP, secretary, treasurer) or the word officer (CEO, CIO, loan officer), he or she is an officer.
As to director, it can refer to two things. First is to members of the board of directors. Second is to a level of non-officer employees typically below the corporate officers and above managers. For instance, the vice president of marketing and sales might oversee the director of marketing who oversees the advertising manager.
These titles may vary significantly by industry and company. For instance, industrial companies typically have very few vice presidents and above, while financial companies will often have hundreds or thousands of assistant vice presidents, vice presidents, managing directors, and senior and executive levels of those, who often will be doing equivalent jobs to what is done by managers and directors (or below) in an industrial company.