Dr. Gershom Bulkeley is a Loyalist. As such, he is loyal to the King of England and upholds the idea of colonial obedience to the crown. He is rewarded for this loyalty by being made a justice of the peace for the colony.
Matthew Wood is a colonist whose Puritan ancestors have been given the right to worship as they wish and settle in the New World to make his living. These rights were stated in the charter granting Connecticut the freedom to practice whatever religions the settlers wish to and freedom to be English citizens living in a colony that is to be self-sustaining. These rights are threatened with a revoking of the charter, so the colonists steal the charter and hide it to keep these actions from occurring.
The two are directly opposite in their political views which will be reflected in the up-coming American Revolution. Even though the two have a falling out, they remain friendly enough to help out in the time of sickness and justice.