Commander in chief and Chief of state

Commander in chief noun - The officer who holds the supreme command.

Chief of state and commander in chief are semantically related In some cases you can use "Chief of state" instead a noun phrase "Commander in chief".

Chief of state noun - The chief public representative of a country who may also be the head of government.

Commander in chief and chief of state are semantically related in chief executive topic. You can use "Commander in chief" instead a noun phrase "Chief of state", if it concerns topics such as government head.