Most media depictions show the American colonists to be distinct from the British by the start of the revolution. In fact the colonists considered themselves British up until the end of the war more or less. They were fighting for better representation within the empire, but the bitterness the fighting took on and British defiance made this impossible. We can see this by what would become the US reaching out to other European powers (France, mainly) and adopting/incorporating some of their system of governance.

The colonists WERE still mainly British though, so language and culture stayed very similar. And the young republic would spend many years arguing over whether allying themselves politically and ideologically with France or Britain was the way to go. The Hamilton-Jefferson rivalry embodies pretty much what the young United States was struggling with at this time.