What Jim Watson said. 19th century ammunition nomenclature is a minefield. (38 S&W was put on the market in the 1870's.) And we are living with the results of 100+ years of mistakes and confusion. Fortunately, places like this website can be a quick way to get things straight.
For example, in the United States, we almost never say ".38 inch" in describing 38 S&W. We would call it "38 caliber". I have no idea how that got started, but apparently at some time caliber had come to mean 1/100 of an inch in the context of ammunition. It is still in general use today, although people have forgotten it is a unit of measurement (maybe). But the true bullet diameter of almost every so called 38 caliber cartridge is actually a trifle under .36 inch. That is why 357 Magnum, which does not fit the caliber system, is called that - it is named after its true bullet diameter. 38 S&W, by the way, is usually said to have a true bullet diameter of .359 inch, but when you are talking about 1/1000 of an inch, things can easily vary.
I started to explain why some people think there is such a thing as "38 S&W Short", but then I realized that would take forever and cause more confusion than it cleared up. Let's just say, as Jim Watson did, that there is no such thing and never has been.