Oyeboten:
That looks to be the genuine article, a 2 inch barreled .38 Military & Police Model of 1905 4th Change manufactured in the late 1930s. Serial numbers in the 651000 range shipped in 1935, in the 680,000 range in 1940. I'm inclined to be romantic and say it was probably purchased in 1939 when the winds of war were blowing and someone decided it was needful to have an insurance policy on hand.
It's the first 2 inch gun from that era I've seen, other than cut down .38 S&W British Service Revolvers. The Standard Catalog of S&W notes 50 to 100 percent premium for the 2 inch round butt if original, 2 inch square butt, double to triple value.
As the Author's have previously stated that the reference in SCSW to the square butt frame with standard length barrel being worth double is a typo and it is the round butt that is worth double, I am inclined to think that there are two typoes in that entry and your gun is worth double to triple.
In excellent plus condition the SCSW gave a value of $450 in 2006 for a 4th change, so potentially yours is worth $1200 or more.
As for the markings on the hammer, I've never seen them before. I'll speculate that the hammer is one made in the 1920s or early 30s for a short barrelled gun as the 1915 patents (ncluding the first generation internal hammer block) were still iin force and S&W would have wanted to claim protection. Some of the longer barreled guns still shipped with patent dates on the barrel during that period. Lacking real estate on the barrel, S&W may have moved the markings to the hammer.
As I am speculating without real facts, I suggest you start a new thread in the firearms research section and see what Old Fuff, Jim Keenan, Oro or Saxon Pig have to say.