Where's difference board chair and chairman?
The chairman of the board and the board chair are exactly the same thing, unless the context is that someone "has a chair" on the Board, which simply means that they are a member of the Board.
I believe a board chair is a person that is a member of a board. The board chairman is the person who is in charge of a board.
A board chair is like a director who is in the board of an organization. The chairman of the board on the other hand, is the highest ranking officer in the board of directors of a firm.