What you're seeing here are the fading memories of what these (not 'the'!) once-United States were meant to be.

You've spent a lifetime embroiled in the results of malignant federalism, to the point neither you nor the people who should have taught you even know what a state is, only what powers the constituent districts called states still have.

To begin with, a state, as the authors of the Constitution and the foot soldiers and generals of the Revolution understood statehood, is a body with a territorial monopoly on the use of aggressive force. From this power, it derives the moral obligation to protect that territory from others and the capacity to enforce laws and levy taxes. You may remember city-states and nation-states from what passes for history classes in this country - the concept is a very old one, compared with the complete subversion in the last century.

A Union of States, then is not one sovereign political entity, (the current federal government) but many independent actors who cede certain powers to representatives of the group as a matter of necessity (national defense, diplomacy, and mediation of disputes).

Prior to the passage of the 17th Amendment, the States themselves chose senators, so they had federal representation accountable to their legislature. Each state maintained a militia, and there was not a standing federal military solely tasked with defending the nation's interests.

As for your question about moving, it was somewhat less of a concern in the 19th century than it is today, but the principles still hold. The state you reside in demands you follow its laws and defend it in times of war, no different than if you moved from the state of Japan to the state of Kazakhstan.