An admiral of the fleet is the highest grade of flag officer authorized in the United States Navy, or a naval officer of equivalent grade in the naval offices of other nations.
Admiral David Farragut.
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Admiral Foote
(As this question is in the WW2 category, this answer is specific to WW2 combatants) "fleet admiral" can refer either to a role, or a rank. As a rank, "fleet admiral" was formally known as "Admiral of the Fleet" in the Royal Navy, Soviet Navy, "Großadmiral" in the Nazi Kreigsmarine, "Fleet Admiral" in the US Navy, and Marshal-Admiral (Gensui) in the Imperial Japanese Navy. In all cases, it was the highest naval rank in each country. Most countries seldom had more than one or two persons serving at that rank at one time. The exception was the US Navy, which had 4 serving Fleet Admirals by the end of WW2. The duties of someone filling the rank of Fleet Admiral generally would be considered Logistical and Grand Strategy - that is, they were almost exclusively shore-bound commanding vast collections of fleets of ships in far-flung campaigns, or heavily involved in naval production and procurement. As a functional role, "fleet admiral" generally refers to the commanding admiral of a specific fleet. It can refer to a variety of ranks of admiral, but, was generally not applied to anyone not at least of admiral rank; those of less than admiral rank who commanded collections of ships were usually afforded the title "commodore". If there were several admiral-ranked personnel in a fleet, "fleet admiral" would be the moniker applied to the one in command (usually the most senior, but not necessarily, depending on circumstances). The role of fleet admiral is a tactical command - it involves directing the operations of the fleet, according to the grand strategy directed by the naval command authority. A fleet admiral would have wide latitude of both action and authority to accomplish their assigned mission(s). Their command usually included not just naval vessels, but transport vessels, naval bases, marines, and sometime even non-Navy assets in the area of operation.
That would be Admiral William "Bull" Halsey of the United States Navy. Admiral Halsey commanded the task force and the Pacific Fleet during WW2 on the carrier Enterprise. He led forces over the Battle of Guadalcanal. He was also made commander of the Third Fleet.
Admiral Farragut
Admiral Patricio Montojo, Commander Naval Fleet Manila. Admiral Pascual Cervera, Commander Naval Fleet Cuba.
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The corresponding naval ranks are normally fleet admiral, grand admiral or admiral of the fleet.
Admiral David Glasgow Farragut was the first American Naval Officer to obtain and hold all 3 Admiral ranks.
Admiral Ernest King was the US top naval officer. Admiral Chester Nimitz was the top Pacific naval officer.
The commander of the Federal naval forces was Rear Admiral Porter. There is no such thing as a naval general.
Admiral Mahan
An admiral of the fleet is the highest grade of flag officer authorized in the United States Navy, or a naval officer of equivalent grade in the naval offices of other nations.
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Admiral George Dewey.