Photos will help us identify the revolvers...
Other than caliber, the definition also includes barrel length as specified by the govt when purchasing, regardless of maker. Unlike requirements of later years where the design and parts were to be identical and interchangable by all makers, such as the Springfield "03, the M1 Garand and Carbine, the M1911 etc, the Civil War era specs were much simpler.
A "Navy" is 36 caliber with a 7-1/2 inch barrel.
An "Army" is 44 caliber with an 8 inch barrel.
As stated earlier, the Naval Battle scene on the cylinder of the Colt 51 Belt Pistol (as called by Colt) is most likely the source of the term "Navy", but all revolvers made on 36 caliber for military use were called Navies regardless of maker.
Although the Colt "Army" also had the Naval Battle scene rolled onto the cylinder, it was not called a Navy. Colt called the revolver a "Holster Pistol", now commonly called a New Model Army. The Dragoon was a "Horse Pistol" as it was really too heavy to carry on a belt, but was normally carried in a pommel holster on the horse's saddle, usually in pairs.
You will find that Colts, Remingtons, Starrs, and others are called Armies or Navies based on the caliber and barrel length.