I'm pretty sure you have an 1899, or in other words, M&P 1st Model. There was a Military contract, which if I'm correct was for chambering to be in the 38 Colt for a Government contract, and S&W just couldn't put "Colt" on the side of their revolvers, so it was named 38 Military. Your gun should have an unsupported ejector rod. It also does not have the screw in front of the trigger guard, is a "pre 5 Screw 4 Screw.
Would look similar to my 1899 which is not a Military contract and has 38 S&W Special on the barrel.
and the insides look like:
