I spend a lot of time forming corporations, so I can chime in on this one.
In the US, corporations (including not-for-profit corporations) are formed under state incorporation statutes. Most state statutes require corporations to have at least two officers: a president and a secretary (who may be the same person). Other officer positions/titles are generally optional, and a corporation’s bylaws establish which other officers–typically a treasurer or a vice president, but potentially chief exalted poobah of marketing (i.e., any titles they want)–a corporation will have. A typical corporation also has a board of directors; the president and the other officers may but need not be directors, and directors are not necessarily officers. The only exception to this is the Chairman of the Board; if this optional office is established by a corporation, this person will always be a director. Since the board of directors has the power to appoint and remove officers and direct the corporation’s affairs, the Chairman of the Board, if there is one, is typically a corporation’s most powerful officer, but is not typically in charge of day-to-day operations.
Regulatory bodies, such as the Securities and Exchange Commission, also sometimes mandate that certain officers sign certain documents. Every public company must have a chief executive officer and a chief financial officer, for example. These do not need to be official titles–the president may well function as the CEO. (Indeed, the proliferation of different titles with different responsibilities attached thereto by various corporations pretty much forces the government to define officers by function.) Given the high profile nature of these regulatorily-mandated positions, however, corporations often establish officer positions called CEO and CFO in their bylaws. This also comes in handy, as others have noted, when a corporation finds it necessary to give important titles to a large number of high-level executives.
Generally, the hierarchy is as follows: Chairman, CEO, President, Executve Vice President, CFO, Senior Vice President, Vice President, Treasurer, Secretary, Assistant Treasurer and Assistant Secretary, remembering always that many officers will hold more than one title (Vice President and CFO), that many corporations will not have certain officers at all and that others may have a key executive with a different title (General Counsel and Corporate Secretary).
Now for the exceptions: not-for-profit and governmental entities (such as many universities) may operate under special enabling statutes or may not be corporations at all. Not-for-profit corporation statutes often permit directors to be referred to as trustees, managing partners or members; this may also occur if the entity is formed as a trust, a partnership or a limited liability company. In these cases, there is so much room for variation that there is no way to know who the ranking officer of an institution is without reviewing either or both of the implementing statute and bylaws (can also be called other names) of the entity. Thus, waterj2 is quite right to look at the University of Nebraska’s bylaws if that university is the entity is question; no other university bylaws will be identical. (I am also ignoring other exceptions from highly regulated industries such as insurance where the Chief Actuary often has real power.)
In sum, corporations and institutions have a great deal of leeway to call their top bananas, chief bottle washers and stategic navel-gazers pretty much anything they want.