Unlike today's weapons requirements for government purchase, where all manufacturers produce interchangable parts, the Civil War era purchasing only proscribed the caliber and barrel length. So a Remington Navy, a Starr, a Colt, Whitney, etc were of 36 caliber and a 7-1/2 inch barrel, without any other parts or features in common.
An "Army" was to be in 44 caliber with an 8 inch barrel, regardless of the maker or gun design. Western travelers liked Navies because they were lighter (certainly compared to a Dragoon) and there were more 80 gr balls to a pound. (almost 90 per pound) The 36 Navy conical bullet (140 gr) weighed the same as a 44 caliber round ball. There were 50 round 44 balls per pound (making it 50 gage)
For purchasing purposes, the 36 Navy and 44 Army were specified by caliber and barrel length, but not by service. Both the Army and the Navy issued revolvers of both calibers.
It might be considered that 50 per pound was the origin of the 44 caliber.
As for actual diameter, the percussion era caliber was identified by the bore diameter before rifling, so it is the land diameter. A 44 caliber groove is 45 caliber, a 36 barrel groove is .38 diameter. In the cartridge era, the bore was switched to the groove dimension calling the caliber, so a modern 44 is closer to 44 (.43) a caliber only used in the metric countries (11mm).. The 45 Colt bullet is the diameter of the 44 roundball.
The 38 revolver is really a .36 because the originals were heel type bullets used in a percussion dimensioned bore, but when the later bullets were sized down to go inside the case, the designation didn't get revised, except as used for the .357 M..