These styles really refer to common situations that many boards may fall into when decision-making is required. However majority support and consensus are styles to which procedures and helpful techniques can be applied. If the board has been allocated one meeting to reach a decision, they may have to choose the most timely method possible. If the decision is to take an hour or 45 minutes for lunch, you don't need to reach consensus to make a decision. However, if the board were to approve a development plan for their community, they would want to spend more time gathering concerns.
Most people typically understand procedures outlining majority support.
However, there are a variety of techniques you can incorporate into the style of majority support to help reduce frustration among members and prevent group divisiveness that often accompanies majority support decisions. This technique borrows from consensus in the sense that a deeper understanding of why members feel a certain way about an action is expressed and helps to develop a shared understanding among board members. It can be as simple as a secret ballot. This technique adds anonymity to who voted for which decision thus reducing potential group divisiveness. One member plays the devils advocate to the potential decision by stating all the opposite possibilities.