What does it mean to say that there were two American revolutions? How were they related?

The event most commonly referred to as the American Revolution is the War of Independence. From 1775 to 1783, the American Colonies fought a war against the government of King George III of Great Britain. The Second American revolution that comes to mind is the American Civil War, which was fought from 1861-1865 during which the southern States declared their independence from the Federal Government and fought a War of Rebellion in order to establish their own autonomy as the Confederate States of America.
The Revolutionary War and the Civil War were both characterized by armed rebellions against the established centralized government. Both resulted in protracted campaigns that inflicted heavy casualties on the combatants and heavy tolls on the populace. They also both resulted in significant course shifts for the direction of the Nation, and left a lasting imprint on the minds of the people of the United States.