test drive,
The serial numbers on the grip frame and under the top strap should match (unless the gun was rebuilt from two separate guns). I'll bet if you wiped the numbers down and cleaned them off a bit - then using a "cheater" (magnifying glass) you'll find that they are the same number. The digits are too close to each other in conformation to be from different guns. Let me know what you find - I've seen dozens of H&R hinged frames where firing gunk/residue has built up under the top strap to the point where the serial number is very difficult to, in some cases, even see, let alone read correctly - I'm willing to bet that the number on the grip frame, which is generally protected by the grip panels, is the correct number. Use a cheater to confirm.
Also, is there a "cartridge" stamp on the left side of the barrel? - it would be either .32 S&W CTG (5 shot) or .22 RIM FIRE (7 shot). Either serial number you posted will, most likely, make your piece a 2nd Model Smokeless powder made in or after 1905 and the presence of that stamping will be definitive.