Welcome to the forum. If your gun has a two-inch barrel, it is called a .38/32 Terrier. Eventually, when model numbers were assigned to the different guns in the company's product line, this gun became known as the Model 32, a designation that has nothing to do with its caliber. Those manufactured between the configuration's introduction in 1953 and the appearance of the model designation are known as Pre-32s.
If it has a four inch barrel, it is called a .38 Regulation Police or, for analogous reasons, a Pre-33.
The odd designation .38/32 just means ".38 caliber revolver built on a .32 caliber frame."
The .38 Regulation Police was introduced in 1917 and remained in production until the onset of WWII. The Terrier was introduced about 1935 as a more compact version of the small-frame five-shot .38 revolver. After the war both models were reintroduced and manufactured with a series of minor evolutionary changes until the much revised Model of 1953 was introduced in -- no surprise here -- 1953. Eventually both models were retired because the market for small .38s was take over by the Chiefs Special (or Model 36) in .38 Special. That gun had a slightly longer cylinder than the Terrier or RP, and eventually the frame got slightly larger too.
The Terrier has a smaller grip than the RP so that it can be more easily concealed in a pocket.
Feel free to post pics of your gun. Whether it is a Terrier or RP, lotes of folks here like those small-frame .38s.