Ed.R.
25
I think...
that the serial number on the case back is unique to your particular watch model (i.e., reference number), and the number on the 3/4 plate is a serial number of sorts for your particular movement.
For example, Caliber 39 movements are featured in several watch models (e.g., Power Reserve Display, Panorama Date, Panorama Date w/Moonphase, etc.), all in a variety of case materials (stainless steel, rose gold, or platinum). Each movement should have its own serial number on the 3/4 plate (mine is 16,000 something). On the other hand (or wrist?), each of these models (in their respective case material) will have its own series of case numbers. Therefore, two Senator Power Reserve Display models, one in stainless steel and the other in rose gold, could conceivably have the same case number (e.g., No. 0025) because they have different reference numbers (as they are made of different metals). Of course, they are powered by two DIFFERENT (identical-looking) Caliber 39 movements, not one movement.
Sorry if my explanation causes more confusion...