The full model name is .38/32 Terrier, and that is what you would have seen on the label on the box it came in. This model was introduced in 1936 and was numbered in the .38 Regulation Police series. In a sense, this model is just a .38 Regulation Police with a 2" barrel instead of 4", and a round butt instead of the larger Regulation Police square butt. It is the design precursor of the Chiefs Special that came along about 1950.
I'd think this gun might have shipped as early as 1938.
Nice early specimen. In the mid 1930s S&W decided there was a potential market for .38 snubbies, and they introduced a 6-shot version on the K frame and this 5-shot version on the I frame. The K-frame gun chambered .38 Special, and the I-frame chambered .38 S&W. After the war they tinkered with the design and dimensions of the small-frame gun to let it take .38 Special as well. In the 1950s the Terrier and the Chiefs Special lived side by side for a while, but the Chief's Special eventually won out -- a little more power in close to the same size package.
Leaving out the top-break models, some of which had similar dimensions, the Terrier was the most compact .38 that S&W ever made.