The US Navy of 1794 was a young and very small Force, consisting of barely 5 Ships and a Force of several Hundred Sailors and Officers. While in time, The Service would grow into one of the largest Navies in The World, in it's fledgling days, even Officers of Rank were identified much different than they would be today. By way of example, the Naval Rank of Commodore, did not exist until The war of 1812. Seen as higher than a Captain, a Commodore was often in charge of a Squadron of Ship and those Officers in Command. Those US Naval Officers that were awarded command of such a Position were referred to a ''Senior Captains''. Between 1812 ans 1818 however, ''Commodores'' were known. After 1818, The US Navy reverted back to Senior Captain. In almost all cases of using Commodores, they were activated during Wartime or the Title was awarded to Senior Captains who had distinguished themselves prior to Retirement. The Rank would be abolished within The US Navy in 1983.
Regarding the identification of a Senior Captain to a Fleet or Squadron, He was awarded His own Flag (not Ensign) to fly from his ''Command Ship''. These Flags were originally of The Pennant design (despite being known as Flags). The first Versions were Blue Fields with a series of White Stars – arranged in a series of vertical Bars. The number of Stars was based on the number of then United States.
Lessor or Subordinate Naval Officers under a Senior Captain (identified by time in Service), also were given flags similar, but these were identified with either a Red Field (1st Subordinate) or White Flag (2nd Subordinate). All Flags were linked to The US Naval National Ensign (flown from all US Warships). After 1899, the use of such Flags was discontinued, as was the Title Senior Captain.