What is a is a region that has its own elected government and voluntaraily associates itself with the US?

A region that has its own elected government and voluntarily associates itself with the United States is known as a "Commonwealth." An example of this is Puerto Rico, which has a degree of autonomy and its own local government, while still being subject to U.S. Federal Laws. Inhabitants of such regions may have U.S. citizenship but do not have full voting representation in Congress.