In 1934 the Ordnance Department of the War Department decided to "modernize" its nomenclature to better organize the huge inventory of new military inventions (notably all the aircraft and armor and transportation equipment).
Rather than rely upon the year of introduction, materiel would be given a Model (some QMC referred to it as a "Military") designation.
This was very much based on wartime experience. Notably, the Browning Model of 1917 machine gun quickly had been followed by an air-cooled version. Also, Browning's Automatic Rifle was also introduced.
So, rather than rely on Machine Gun, Cal..30 Water-cooled, Model of 1917, and Machine Gun, Cal..30 Air-cooled, Model of 1917, and Rifles, Automatic, Cal..30, Model of 1917--they became the Model of 1917, Model of 1919, and Model of 1918, respectively. That was a well remembered mess. Which was getting worse with all the models of tanks, aircraft, trucks and the like all coming out, and often more frequently than once per year. Tank, Light, Model of 1922, Early and Tank, Light, Model of 1922, Late were just not going to work once you started adding "A" variants on (consider a Light Tnak Model of 1922A3--which version?)
So, all materiel would be numbered sequentially from 1, per category of thing. So, starting in 1936, you did have some confusion. There was the M-1 Rifle, Cal..30 Semi-Automatic; and a M-1 Howitzer, 105mm; or the M-3 Light Tank, M-3 Medium Tank and so on.
Eventually it works out. There was an M-1 Carbine. Later an M-2 Carbine, and an M3 Carbine after that. Around 1990 we saw the 4th official Carbine, the M4. Trucks are well up into 4 digits. Every so often, DoD will "reset" the numbers, as they did in the 70s, ending the "century series" of fighter aircraft at 111, and resetting to F-12 (none were adopted until the F-14, but the sequence has carried on from there).
So, "M" for Model has a long history, closing up on a century here in a bit more than a decade.