Which state was neither part of the confederacy or the union?

The two states were Delaware and Maryland.

The so called border states were states that did not declare a succession from the Union and did not join the Confederacy. They bordered the free states of the Union to the north and the Confederate slave states to the south.

Four other states did not declare succession until after the battle of Fort Sumter and they were briefly considered to be border states: Arkansas, North Carolina, Tennessee and Virginia.

The border states were bitterly divided about secession and were not eager to leave the Union. Their biggest concern was the military coercion of the Confederacy.