Which order communicates the commanders' intent and initiates tasks for subordinate commands?

The Execution Order is the correct choice because it serves as the formal directive that outlines the specific tasks and responsibilities for subordinate commands. This order conveys the commander's intent clearly and concisely, ensuring that all involved parties understand the objectives and the operational plan necessary to achieve them. It also delineates the timelines and resources required for the execution of the mission, making it critical for operational success.

In contrast, other options serve different purposes within the military planning process. The Concept of Operations (CONOPS) provides a broad overview of the planned operation, focusing on intent rather than specific tasks. The Deployment Order communicates the details regarding the movement of forces but does not typically include the execution specifics. The Planning Order is concerned with the preparation of plans and does not initiate actions or tasks. Thus, the unique role of the Execution Order in actual task initiation and communication of intent distinguishes it as the correct answer here.