A high-ranking naval officer; used for both historical and modern contexts. In modern usage, typically refers to an admiral, while commodore is a lower flag rank.
He was promoted to admiral in the navy.
The admiral is commanding the fleet.
He was appointed admiral at a young age.
He commanded the fleet as admiral.
司令官 is a broad term for any commanding officer, while 提督 is reserved for high naval rank such as admiral.
海将 is the modern Japanese Self-Defense Force rank equivalent to admiral, while 提督 is the more traditional or general term for the same rank.
総督 and 提督 share the kanji 督 but 総督 is a civil governor-general while 提督 is a naval admiral or fleet commander.
From Chinese 提督 (tídū), originally a military title. The characters mean 'to lead' (提) and 'to supervise' (督).