Southern Definition
A clear indication of the difference in thinking can be seen on the Confederate battle flag. A quick examination of the stars on the flag shows thirteen stars. The list on the left shows only eleven seceding states. So obviously the South considered two states to be a part of the Confederacy that were not that all that clear. The two states in dispute were Kentucky and Maryland.
As a slave state Kentucky played a role as a supplier of slave labor to the deep South. But the Union firmly took hold of Kentucky in late 1862, so it would be difficult to claim it for the South. However, southern sentiment was strong in some areas of Kentucky, and as many as 25,000 soldiers joined the Confederate Army from that state. Had Kentucky clearly fallen into the Confederacy many more men would have been available for service. By contrast Kentucky funrished 75,000 men to the Union Army.
Maryland was also a slave holding state and faced many of the problems that were evident in Kentucky. Maryland had the added problem of proximity to Washington, DC. The Union needed Maryland as a buffer, and for that reason claimed Maryland early in the conflict.