A senior Captain, usually on track for Admiral, with more than one ship under his overall command. (My memory)
Wiki: An American commodore, like an English commodore or a French chef d'escadre, is but a senior captain, temporarily commanding a small number of ships, detached for any special purpose. He has no permanent rank, recognized by government, above his captaincy; though once employed as a commodore, usage and courtesy unite in continuing the title.
A senior Captain, usually on track for Admiral, with more than one ship under his overall command. (My memory)
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A Commodore was a 1 star Admiral back in the day when the Navy Captains went directly to 2 Star Admirals...Which ‘rankled’ them (USN Captains) when in a Joint Command (Pentagon for example) while a 4 Striper (USN CAPT) could actually be Senior to a 1 Star General Army/AF/USMC type.
The ‘it’ really hit the fan when the Navy Capt finally got to put on his ‘Stars’ and reported to work the following day with TWO Stars, while the 1 Star ‘others’ still had one star)
A USN Commodore in the fleet is ANY Officer who commands a squadron, in my LST days, the Commodore was a Full Commander, usually either getting ready to retire or on verge of making Captain.
We would address him as Commodore, the same way we addressed our Lt Commander or Commander COs as Captain.
As to ‘piping aboard’,
“””COMMANDER, LST SQUADRON 9 ARRIVING””” (Squadron CO)
“””TERRELL COUNTY ARRIVING”””(Ships CO)
In Commonwealth countries (Australia, the UK, Canada, New Zealand,etc) it is a 1 star rank. It’s a better sounding name than Rear Admiral Lower Half.