Director is a recognized title. Ususally, "director" is followed by "of", then the department. i.e. Director of marketing. However, I have never heard of "Director At Large". Of course people can create their own titles on their business cards.
Board of Directors have the overall responsibility for supporting and monitoring the performance of the President, clarifying the Club mission, forcing forward thinking and approving long range missions, monitoring programs and activities for appropriateness, conformity with mission and achievement of expected outcomes, ensuring financial solvency, preserving institutional independence, enhancin