could this also be 'the chairman has relationships?' Duolingo did not accept chairman in this sentence. I don't see the distinction between board and chairman.
Yes, you're right. 'Der Vorstand' can also mean 'the (male) chairman'. In that case, it's a synonym of 'der Vorsitzende'. It can also refer to any male member of the board. Note that this doesn't work for female members or chairs of the board. In that case you have to use 'die Vorsitzende' or 'das Vorstandsmitglied'.