Howdy
The number on the butt is the Serial Number, the number on the frame under the yoke is an assembly number
According to the Standard Catalog of Smith and Wesson, the 1D serial number series was limited to the Models 64 and 65, so that actually makes this one pretty easy. Both of these revolvers are built on the stainless K frame with fixed sights.
The Model 64 is a stainless version of the standard Model 10. It is chambered for 38 Special and has fixed sights. It came with a 2" barrel and round butt or 4" barrel and square butt.
The Model 65 is a heavy barreled 357 Magnum revolver. It came with a 3" barrel and a round butt or 4" barrel and square frame. I don't have a photo of a Model 64, but this is a photo of a Model 65 with after market rubber grips.
Seeing as yours is chambered for 38 Special, I'd say it is a Model 64. The Serial Number range for 1979-1980 was 1D45001 through 1D99999. So that tells you when yours was made.
By the way, a revolver of that age should tell you exactly what it is. The model number should be stamped on the frame under the cylinder yoke. It should say something like MOD-64. If it doesn't then something does not compute.
