First off, that gun is not military, it is the civilian model. It was called the Army and Navy Revolver, but Colt never assigned model numbers to its civilian guns. The Model 1892, etc., are military designations. Changes to the civilian guns tracked changes to the military guns, but Colt did not change the civilian designation.
As to the various model numbers and what they represent, it is confusing, but I will take a crack it.
First, the Model 1889, also called the New Navy revolver, locked up at the rear of the cylinder; there are no notches in the outer surface of the cylinder. Its deficiency was that when the trigger was released, the cylinder could turn, possibly resulting in a second attempt to fire the same chamber. The Model 1892, though appearing very similar, was improved, with the cylinder having two visible notches. The first was engaged by the top of the trigger to stop cylinder rotation. The second (front) engaged the cylinder when the trigger was released. A projection on the cylinder latch kept the cylinder from turning backward under pressure from the downward moving hand before the front cylinder stop engaged.
The system worked reasonably well, but wear on both the ratchet and the cylinder latch was high and often results in the guns not functioning correctly.
The Model 1892 gave reasonable service, but one complaint was that the gun would fire with the cylinder not quite closed. So the Model 1894 added a locking lever, which prevented the hammer from being cocked unless the cylinder latch was in the forward position (Frank B. Felton patent 535097, March 5, 1895. The design had actually been worked out in 1894 and was being installed on Model 1894 contract guns prior to the formal issuing of the patent). A screw end just under the latch indicates the presence of this modification.
The Model 1896 was the same as the Model 1894 except for strengthening the hand and bolt springs. There are statements made that the rifling and/or bore dimensions were changed at that time; this may be true, but I don't have both models for a comparison.
The Model 1901 was the same as the Model 1896, but has a lanyard ring. The Model 1903 is like the Model 1901 but has a shorter grip (front to back) and thinner stocks.
The Model 1905 USMC revolver is the same as the Model 1901, but has a rounded butt and a lanyard loop.
Wow! To add to the confusion, the Navy bought quantities as it had the money and took whatever Colt was making for the Army at the time, giving the guns a Navy model number. All the while, Colt was making civilian guns, tracking changes with the military model. Civilian models, for some reason, had a shorter (front to rear) and slightly differently shaped butt.
Then (do I dare go further), the Army and Navy kept upgrading the guns, the Navy even having Colt upgrade 1889 models to the 1894 configuration.
In any event, the .38 caliber failed rather miserably in the Philippines, and the Army once more went to .45 caliber, adopting the Model 1909 revolver, which would be supplanted in a short time by the Model 1911 auto pistol.
Much of this information comes from the book "A Study of Colt's New Army and Navy Pattern Double Action Revolvers 1889 to 1908", by Robert Best. The knowledge of the internal workings and the problems with the guns comes from personal knowledge, learned from frustrating experience trying to time those blankety blank guns.
Jim