The first thing you need to understand is that this "1st change," "2d change" etc., stuff is entirely artificial. That isn't to say it is "wrong," but that it was invented by a couple collectors in the 1930s to help collectors identify engineering changes that were made to various models over time. These are not model designations per se and were never used by the factory, nor did that language appear contemporaneously with the guns. They are strictly collector-speak.
With respect to the .32 Hand Ejector, S&W made the First Model in 1896. A redesign was implemented in 1903 and that became the Second Model, or Model of 1903. There was no alteration of that basic design again until 1919, when the Third Model was released. It looked the same as the Second Model externally, but the lockworks were improved significantly with the addition of the new hammer block safety device.
The Second Model lasted from 1903 until the end of 1918. Yes, there were engineering improvements during those years and collectors like to make note of them. But they were not considered model changes by the S&W company. An analogy can be made with more modern guns - for example, the .38 Combat Masterpiece. You see the Model 15-1, Model 15-2 and Model 15-3. Engineering changes are reflected by the dash numbers, but it is the same model gun.
I hope this helps.
