All has been made clear. You do not have a Model 10 or its predecessor the Military and Police model. You have a Regulation Police model exactly as it says on the barrel. Completely different model. The Regulation Police was built on the slightly smaller I frame, rather than the K frame of the Military and Police model. Most obvious should be the Regulation Police was a five shooter, because it was built on a frame designed for a 32 caliber revolver. The M&P was a six shooter because it and its cylinder are a little bit larger.
Your revolver is chambered for the 38 S&W cartridge, exactly as it says, not the 38 Special or 38 S&W Special cartridge. The 38 S&W round is the one on the left in this photo, the 38 Special (or 38 S&W Special) is the one on the right. You should not be able to chamber a 38 Special in your revolver, it should be too long. Unfortunately, even though the 38 S&W round was a few thousandths larger in diameter than the 38 Special, sometimes because of this a 38 Special will chamber in a 38 S&W revolver. Do not attempt to fire 38 Special ammo in it, only the shorter 38 S&W round.
The 38 Regulation Police was made from 1949 until 1974, Serial Numbers ran from 54475 to 122678, so yours is quite early. In 1955 the Regulation Police was renamed the Model 33. At some point the frame was changed from the I frame to the more elongated J frame. Post a photo and we can tell you which frame you have. And count the chambers, I'll bet there are only five.
P.S. Don't try that Buffalo Bore ammo. You have an old gun there. Stick with regular SAAMI spec ammo. On the plus side, the Regulation Police is a smaller revolver than the M&P/Model 10 and is more concealable. Funny thing is, many police departments depended for years on 32s and lightly loaded 38s, by modern standards. But during the 1930s when gangsters started driving cars police departments felt they needed something more powerful. Not that gangsters were tougher, the police had to shoot through car bodies and were trying to stop the cars by shooting out the engines. That's why the 357 Magnum was developed.