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The Continental Army fought during the American Revolution when the 13 colonies were separate states. What passed for a central army was really a collection of the militias of the several states, and were raised and paid for by the individual states.
The Legion of the United States, the predecessor of the U.S. Army was formed in the 1790s, after the 13 colonies had ratified the Constitution, and joined to form the United States, so it was paid for from the central (US) Treasury.