The Declaration of Independence signaled the formal beginning of the Revolutionary War, with the Thirteen Colonies separating from Britain. In this respect, it was a critical moment in US History, representing the beginning of the Revolutionary War (and the beginning of the United States as a country).
At the same time, in practical terms, armed hostilities between Britain and the colonies had already began (the battles of Lexington and Concord were fought in 1775), and the history of tension between Britain and the colonies could be traced back even farther than that. The Declaration of Independence entailed a formal recognition and justification of a state of rebellion that (I think you can argue) preceded its existence. (In that respect, it simultaneously represents both a continuity and a turning point.)
At the same time, I would say some of the largest continuities could be found on the social and economic levels. After all, consider that a farmer would have been no less a farmer after joining the Revolution. In short, there are certain key elements of personal and collective identity that would have remained largely constant across both sides of the Revolutionary divide: matters of religion, occupation, and ethnic identity, to give a few examples.
Despite the fact that the revolution was a dramatic political transformation, I think there would have been powerful economic and social continuities running across the entire time-frame, largely consistent across both sides of that divide.