Parallel to and reflecting this framework for operations are organized elements within the armed forces which prepare for and conduct operations at various levels of war. While there is a general correlation between the size of units, the area within which they operate, and the scope of mission they perform, the correlation is not absolute. In fact, it is ultimately the mission that a unit performs that determines the level of war within which it operates.
— David M. Glantz, Soviet Military Operational Art
Campaign: this describes either a subset of the theatre of operation, or a more limited geographic and operational strategic commitment, such as the Battle of Britain, and need not represent total national commitment to a conflict, or have broader goals outside the military impact.
Battle: this describes a subset of a campaign that will have specific military goals and geographic objectives, as well as clearly defined use of forces, such as the Battle of Gallipoli, which operationally was a combined arms operation originally known as the "Dardanelles landings" as part of the Dardanelles Campaign, where about 480,000 Allied troops took part.