The War Department sometimes made errors, usually due to lack of information. For instance, Russell's Partisan Ranger Battalion from NE Alabama was accepted by the War Department as the 15th Tennessee Partisan Ranger Battalion.
There wasn't any general order naming one unit as Confederate and another as Tennessee. The War Department received submissions for service in the mail. If the officer submitting the request wasn't clear about the state his command represented, or if more than one state was involved, commissions were issued as a 'Confederate' command with a number assigned by the War Department. Otherwise, the command was given a numerical designation under the state it was supposed to represent.
War Department correspondence would resolve most questions. There are tens of thousands of letters and documents containing all kinds of information, much of it on microfilm.