Is a 501 c 6 association required to include both a board of directors and officers as part of their bylaws?

This is not a legal answer. You can ask an attorney about the specifics of a 501(c)(6) corporation, and its structure and board requirements.

In a condominium association, a legal corporation -- read your governing documents to verify this -- usually, the membership elects directors. The directors agree among themselves which office each will hold. Every office is held by a director.

The director is a person; the office is a position with a series of responsibilities. So not only do you need both, they are one and the same. Also, then, a director is an officer; a president, a vice president, and so forth.