The model 34-1 is a J - frame. Model 34 (no dash) are I - frames.
From Wiki -
The Smith & Wesson Model 34 Kit Gun is a small, 6-shot, .22 Long Rifle, double-action revolver made by Smith & Wesson. It came with a 2-inch or 4-inch barrel and has adjustable-sights. It was designed to be easily packed in a hunting or fishing "kit" for small game hunting, plinking, pest control and self defense.
History
Smith and Wesson Model 22/32 Kit Gun
In 1911, the Kit Gun line began as the 22/32 an I-Frame, .22LR, 6-shot revolver. These are sometimes called the "pre-war" models.[1] In 1953, an improved model was introduced, the "22/32 Kit Gun, Model of 1953”. In 1958, Smith and Wesson renamed it the Model 34. This production line continued until 1960, when it was redesigned using the slightly larger J-frame and marketed as the model 34–1.[1] The Model 34 continued to be manufactured until 1991.[1]