A board of directors and a board of trustees have similar structures and purposes, both conducting oversight and governance activities within an organization. The primary difference is the type of organization in which each board operates.
A board of directors, also called a "directorate," is a governance panel that manages the general business activities of a publicly traded company; that is, a company with shareholders. All publicly traded companies must have a board of directors.
Shareholders vote on board of directors membership. Usually this is done through mail by a proxy statement, although shareholders have an option to cast the vote in person at the annual director’s meeting.
The purpose of the board of directors is to handle oversight of the company’s business activities conducted on behalf of the shareholders. This includes deciding when or if to pay out shareholder dividends.
Members of the board of directors receive compensation in either cash, stock, or both.
A board of trustees is similar to a board of directors. A board of trustees, however, operates in the context of a nonprofit organization.
A good example, provided at Investorglossary.com, is that of a mutual funds group. The mutual funds group itself, a shareholder entity, has a board of directors; whereas each of the individual funds, as a nonprofit, has a board of trustees.