Commander in chief

A commander in chief (abbreviated CinC or CINC) was the supreme commander of an entire military or other type of service organization. If the person occupying this position was within the military hierarchy, they were the senior flag officer and by definition had the highest service rank possible.

On Earth, the President of the United States also served as the commander in chief, a role Abraham Lincoln fulfilled "during the four bloodiest years" of American history. 

Starfleet's commander in chief was a position held by the senior fleet admiral, who took orders only from the Federation Council and its president. 

In the mirror universe, $𝜇$ rose to the position of commander in chief sometime between the 2260s and the 2360s. 

Background information
The commander in chief of Starfleet named "Bill" in Star Trek VI was played by Leon Russom, and was never identified by his full name. In the script, however, he is labeled as the "Commander in Chief". (The novelization of Star Trek VI established his last name as Smillie.) His uniform was notably different to that of other flag officers by having two stripes of gold piping around the tunic flap instead of just one (as the other admirals and commodores wore), three gold soutaches on his pants stripe (as opposed to one for commodores and admirals and two for fleet admirals) and a much larger fleet admiral insignia on his sleeve.

Fleet Admiral Harry Morrow, who was identified as "Commander, Starfleet" in, might have been the commander in chief of Starfleet. The Star Trek III novelization establishes that he was and the Star Trek IV novelization establishes that Cartwright had succeeded him during the time Kirk and crew were on Vulcan.

In a later production,, the Federation President, Jaresh-Inyo, identifies himself as Vice Admiral Leyton's "commander in chief." This could mean that the president has the right to consider himself "commander in chief of the Federation", or its services, even though the post of "commander in chief of Starfleet" was a separate position within the subordinate organization. It could also mean that the Federation had a similar structure to the current United States with civilian overview by the president serving as commander in chief, and theater-wide commanders also known as commander in chief. In, Leyton, whose title is Chief of Starfleet Operations, does not seem to have any superior other than the president, so his position seems equivalent to the earlier commander in chief. It should be noted that when Admiral Kirk held the position of Chief of Starfleet Operations, he did have a superior, Admiral Nogura.

The possibility also exists that a person who has risen to the position of commander in chief of Starfleet might also be allowed to run for and be elected to the position of Federation president, holding both offices simultaneously. However, the enormously difficult division of labor and potential conflicts of interest which would result seem to make such a scenario unlikely. Moreover, according to Leyton's accusation and his own admission, President Jaresh-Inyo was not particularly adept at or enamored of military affairs, a fact that subverts the possibility of him holding both the offices of president and Starfleet commander in chief simultaneously.

In the It's A Wrap! sale and auction, a rank braid was sold, with its information indicating that it was created for use in the movies, but was ultimately unused.

Stabschef der Sternenflotte Commandant en chef 宇宙艦隊最高司令官 Commander in chief