Do you realize that the United States, as it exists today, is the third country to be called the United States of America?
In the beginning we were British. It is one of those little inconvenient truths of American history that we have to live with and sometimes forget. It was just one really big unhappy empire. Their government was ours. Their people were ours. It, because of our remote nature, was never a really happy arrangement. This does not obviate the fact that we were the same people of the same country.
Then, for reasons I won't explain here, came the Declaration of Independence and the Revolutionary War against the British, followed shortly by the first United States constitution—The Articles of Confederation.
That country, as it existed in the beginning, was the United States, Version 1.0. It's constitution was only enough to keep the several States together and participating in the war effort.
Incidentally, when the Colonies were finally granted their freedom by the British, they did it by granting independence to them, individually, naming all thirteen colonies as independent countries. More than that, under the Articles of Confederation, the States were regarded as different and separate countries. They even had different money from State to State. The only drawback was that the system under the Articles of Confederation wasn't working very well and they were in imminent danger of falling apart and being conquered on all sides.