Yeah, so "The Board" is actually The Board of Directors, right? If you are on the board, you are a director. You can be Chairman of the board, Chair of the Board, Vice President of the Board, Treasurer of the Board etc. and still be a "Director". Kinda like being a politician. You can be a Senator, a Councilor, a President etc. and you are still a politician.
The two referenced titles are not mutually exclusive.