"US media figures are in the habit of referring to the president of the United States as the “Commander in Chief of the United States”
People who do that badly misunderstand the structure of US government as described in the Constitution of the United States. This misunderstanding may have been caused by the disappearance of “Civics” (government) from state mandated high school curricula over the last few decades.
In fact, the president “wears two hats,” hats that are separate in function and scope of authority.
The constitution makes it clear that the president is commander in chief of the armed forces of the United States. As such the armed forces are subject to his orders. The only limits on his authority over the armed forces are those established by federal law. Some examples of acts beyond his power would be controls over methods of acquisition of materiel and the weak restrictions placed on his powers by the War Powers Act. Nevertheless, in general, the president orders the armed forces to act and they then act." Lang