I believe they used Confederacy to denote a clear difference between state and federal government and recognize each states sovereignty.

U.S. Constitution

"We the people of the United States, in order to form a more perfect union"

Confederate Constitution

"We, the people of the Confederate States, each State acting in its sovereign and independent character, in order to form a permanent federal government"

"Permanent federal government" is rarely mentioned by Southern historians and was a corner stone of their law.

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David Upton