As they say, a picture is worth a thousand words…
The revolver is a
Colt 1892 New Army/Navy model. They were made from 1892 to about 1907, with the terminal serial number being 291,000. As you can see the one you have is one of the last ones made.
Most of those that were made to use a .38 caliber cartridge were in .38 Long Colt, not .38 Special. But I have handled one that was in the same number range as your gun, and it was a .38 Special. Those that were intended to be used with the .38 Long Colt round have chambers that are bored straight through; so end-to-end they are the same diameter. The relative few that were made in .38 Special have chambers that are stepped down toward the front, so the diameter at the back is slightly larger then at the front.
Someone replaced the original barrel with one that was intended to be used on a much later Official Police revolver – yes, it would fit.
Returning to the chambers, .38 Special cartridges will easily fit in a chamber made for the .38 Long Colt, but at the front the throat is way oversized for the bullet. If the cylinder was originally chambered in .38 Special with the smaller throat at the front this wouldn’t be a problem.
But the revolver, except for the barrel, is over 100 years old. If you intend to shoot it I would be very careful when it came to selecting ammunition. Just because a cartridge will go into a chamber doesn’t make it the right kind to use.