You have a Colt New Navy revolver.
In 1889 Colt invented the modern double action swing-out cylinder revolver.
It was first bought that year by the US Navy, and in 1892 the Army also bought it.
The Navy version is recognized by not having cylinder locking notches on the outside. The Army model had two rows of locking notches on the outside of the cylinder.
These were made in various upgraded versions until 1907 when they were discontinued.
These were made as both US issue guns and as commercial sales guns.
US Army and US Navy issue guns will be stamped as such on the bottom of the butt along with the serial number.
Commercial models will have only the serial number, stamped in two lines on the butt.
US issue models were chambered in the .38 Long Colt, commercial guns were in .38 Long Colt, .41 Long Colt, and after about 1903 in .38 Special and .32-20.
It was the New Army Model 1896 in .38 Long Colt that failed in the Philippines and led to the adoption of the .45 Automatic.
As above. the serial number is stamped on the bottom of the butt for both military and commercial guns.
The other numbers are factory assembly numbers used to keep fitted parts together during manufacture.
If the serial number is not on the butt it's been ground off. This is not uncommon with military issue guns.
A missing serial number means the gun is illegal to possess.
I suspect you have a commercial New Navy model.
You can buy an Archive letter from Colt that will tell who the gun was shipped to, and if it was factory engraved and plated.
Normally the military models shipped with smooth walnut grips, the commercial models shipped with black hard rubber grips with molded in checkering and Colt logos.
https://www.colt.com/Customer-Services/Archive-Services
Here's some more info on the Colt New Army & Navy models:
http://www.coltfever.com/New_Army___Navy.html
NOTE: The .38 Long Colt IS NOT suitable for use with ANY .38 Special ammo unless it was made after about 1903.
You can still buy .38 Long Colt ammo from the cowboy ammo makers, and you can shoot very light loads in .38 Special brass, but since the Long Colt barrel's bore is large then the .38 Special, accuracy wouldn't be great.
Due to the fragile action, unless these are in really good shape and gunsmith inspected, they're best to be used as display guns.