S&W abandoned the Model of 1905 (and Model of 1902) terminology in 1915. Thereafter, the same revolver was called the .38 or .32-20 Military and Police Revolver (square or round butt) in all company catalogs and advertising. Insofar as S&W was concerned, the "Model of 1905" effectively ceased to exist. However, there remain many collectors who continue to use the Model of 1905 terminology for all similar revolvers made up to WWII. It is not really incorrect as the revolver itself remained much the same as it was in 1905 (but for several engineering design modifications) for the whole time. But the fact remains that "Model of 1905" is not what S&W called it. I cannot explain exactly why the historical letters continue to call those post-1915 revolvers as Models of 1905 because I do not know. Perhaps somebody reading this is aware of and can explain the reason. Maybe it's just tradition. Similarly, the fourth and earlier "changes" were never part of S&W's factory nomenclature system. They are purely collector terms. Yet they appear in historical letters and are also in various reference sources just as though they had been used by S&W.
I'll take a shot.

I collect M&Ps. I have a bunch. I have never really counted them, so I don't currently know how many. A few duplicates were sold occasionally so I could afford to buy others I didn't have or were sold when I just needed money.
I am a student of the M&P.
I have always desired to understand the mechanical evolution of the M&P. I have disassembled and studied every mechanical and model variant of the M&P. A very interesting point in the evolution of the M&P is the fact that unlike many design changes made by manufacturers to make a product
quicker and
cheaper to manufacture, many changes to the S&W action were incorporated to make the gun
better, not quicker or cheaper. I am certain some changes made them more expensive to build. That is a laudable philosophy.
But back to your question-
Being a
student and
collector of the M&P, I wish to own and understand all mechanical variants of the M&P. So, when I'm playing with my guns, it truly does matter to me whether I am holding a 1902-1st Change, or a 1905-1st Change, or a 1905-3rd change. I can tell at a glance or even by feeling in the dark whether I am holding a round butt or a square butt, so the "
1902 or 1905" controversy is pointless to me.
WHAT is the gun mechanically?
I own at least one of all mechanical variants, so the whole point for me is exactly which variant I am looking at.

It is even more fun when you've examined enough of them to note that there are variants with mixed features of the "changes", like an 05-2nd that still has the keyway in the frame, but lacks the key on the rebound slide. Or an 05-3rd that still has circular ends on the extractor star......