The S&W K22 was/is the .22 LR chambered target K frame revolver. It was introduced a few years after WWII ended with the new "short action" K series. At this time, S&W did not used model numbers to identify it's j, k, and n frame revolvers.
The model 17 was the designation for this revolver after S&W started identifying it's revolvers by model number in late 1958.