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And quick answer is that the "battle plan" is the end result, the product, of planning for a battle.
operations
Lines of Effort (LOEs) and Lines of Operations (LOOs) are concepts used in military planning but serve different purposes. LOEs organize tasks and objectives around a common goal, focusing on achieving strategic outcomes across various domains, such as political, economic, and social. In contrast, LOOs refer to the physical paths or methods through which military forces achieve their objectives, often emphasizing the movement and maneuver of troops and resources in the operational environment. Essentially, LOEs are more about strategy and goals, while LOOs focus on the tactical execution of military operations.
There is no difference I know this because I am smart
They have no life.