Things get real confusing on the names of those revolvers. The first New Navy was adopted by the Navy and called by them the 1889 model. Colt called it the New Navy in their advertising. (Presumably the "Old Navy" was the Model 1851.)
Then the Army demanded changes to the New Navy, and adopted it in 1892 as the Model 1892; Colt called it the New Army. (The "Old Army" I assume was the 1873, but who knows the mind of an ad writer?)
Then the Navy decided to adopt the New Army as the Model 1895; Colt kept calling the civilian version the New Navy, even though they stopped production on the old New Navy and all the civilian guns were like the New Army. To satisfy requests for the New Navy, they simply used the old Navy type grip pattern (COLT in an oval) on the "Navy" guns, and the rampant Colt on the "Army" guns. Advertising used the words "New Army and New Navy" or sometimes "New Army and Navy", the term commonly used by collectors.
Then, around 1903, the chamber shoulders on both contract and civilian guns magically disappeared and the barrel dimensions were changed. The change was made to the service guns with the Army Model of 1903, to civilian production in early 1904. Now the Colt guns could the new .38 S&W Special cartridge, but Colt, of course, never used those hated initials or changed the barrel marking. (Needless to say, those old revolvers should be fired only with .38 Special standard loads, not +P or +P+.