Of the three calibers you mention, I would think the 9 x 19 mm Para would lead the list. I have a good, but not great, collection of that caliber with over 6,000 specimens in it. I don’t collect dates or lot numbers in that collection. My .45 Auto collection is better than my 9 mm one, and I DO collect dates in that caliber, and I have only somewhere around 2,200 specimens. Of course, really good collections of 9 mm could easily double, or more, that 6,000 number, while the .45 could probably increase the at least 25%, but still would be considerably less in numbers than the 9 mm.
The .38 Special has been around since 1899, if my memory serves me correctly, and it is still “alive and well,” but I have no concept of the variations. Since its widespread use was pretty much limited to the USA (note the word “widespread”), and the 9 x 19 mm is virtually a universal cartridge now, both militarily and commercially, I would think that there would be no question that is the most widely manufactured, with the most variations, of all the auto pistol & submachine gun cartridges.