I know states' rights advocates revere the 10th Amendment. But when the word "states" appears in the Constitution, it typically is part of a compound word, "United States," or refers to how the states and their people will be represented in the national government.
Before the Civil War it was, "These United States."
Yes. Crucial distinction. We were once a federation of sovereign states. Lincoln turned us into a single government with state-level partitions.