Many older guns use Assembly #'s to help get the correct parts back on the correct firearm after they have been put through the final finishing.
These Assembly #'s may "sometime" (depending on the Maker) be the last three or four digits of the actual serial #.
The actual Serial # maybe either on the bottom of the grip or under the grip panel, stamped on the inside of the grip strap.
I hope this helps.
My best,
Blair