My answer to a Quora question:
The chief executive officer is “A corporation's highest-ranking administrator or manager, who reports to the board of directors.” CHIEF EXECUTIVE OFFICER, Black's Law Dictionary (10th ed. 2014).
The chairman is “The preeminent member of a board of directors, responsible for leading the firm's other officers and executives, presiding over board meetings, and ensuring that the firm's duties to shareholders are being fulfilled by acting as a link between the board and the upper management.” CHAIR OF THE BOARD, Black's Law Dictionary (10th ed. 2014).
“Chairman Williams stressed the different roles that the chair and CEO have to perform: ‘[I]n the board environment, the role of the chairman . . . is to create the kind of open, contributing and questioning environment . . . The CEO's role is to speak for management.’” Joel Seligman, A Modest Revolution in Corporate Governance, 80 Notre Dame L. Rev. 1159, 1176 (2005).
“The roles of the chairman and CEO can be seen as encompassing different domains that may not be complementary, particularly if one of the roles of the chair is as a mentor and reality check for the CEO, and as a focal point for providing information to the board as a whole.” Mark A. Fox et. al., Corporate Governance Research on New Zealand Listed Companies, 29 Ariz. J. Intl. & Comp. L. 1, 31 (2012)