When we talk about "right wing" and "left wing" in military terms, we aren't discussing liberal vs. conservative.
To better understand the terminology, think of yourself facing someone and extending your right arm for a handshake. The other person has to reach across his or her own body to shake with a right hand.
Your left hand is actually opposite that person's right.
And so it was with armies during the Civil War. When they aligned across a battlefield, the left of an army faced the right wing of their opponent.
Gunfire directed from a flanking position along the length of an enemy battle line. Enfilade fire was particularly effective with artillery. Canister could be used to take out whole sections of advancing infantry.
Regiment: military unit composed of 10 companies and led by a colonel. A company was usually between 80 and 100 men. A regiment usually had between 860 and 1,000 men. It wasn't uncommon for a regiment's battle force to be half of what it should be.
Brigade: an organized military unit that was generally composed of five regiments and led by a brigadier (one star) general.
Division: military unit composed of three or four brigades led by a major (two star) general.
Corps: large military unit composed of three divisions led by a lieutenant general (Confederacy) or a major general (Union).
Where did this fighting occur?
The opening portion of the Battle of Stones River occurred primarily in the area defined by Franklin Road (Old Fort Parkway), Gresham Lane and Wilkinson Pike. Medical Center Parkway cuts through the area near the Old Harding House and the brick kiln. Modern Thompson Lane bisects the area as well.