Using the part of Neal & Jinks naming convention I like, the gun would be best called a 38 Hand Ejector, Military & Police, 1st Change that likely shipped from the factory in 1907 or 1908. That way, no issues with 1902/1905 differences.

For me, the gun was heavily buffed and poorly re-blued, but I bet if functions and shoots just fine. Also, looks like some pitting on the hammer sides? Original finish guns are most commonly identified by very crisp and sharp edges, no dishing or rounding of the edges of the revolver. Second, all parts would be the same color. It appears that part of the gun is plum and part is dark blue. That will happen with dissimilar metals that were not left in the bluing solution long enough. My understanding is that the harder the steel, the longer it should remain in the bluing tank.

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Gary
SWCA 2515