If you are looking at the current offerings there are some noteable differences. IMO the 625 PC is suited to shooters who don't like to "tinker" with their guns, the 625 JM is for shooters who make it a habit to do a bit of "tuning" on any new gun they purchase. Now for some specifics. Note, both current models feature 4 inch barrels.

625 PC. Features a broach rifled barrel with a "light" profile, meaning the underlug is cut back to reduce weight. Trigger and hammer are "blued" Forged with a smooth trigger that features a trigger stop and a special "service" width hammer with a teardrop hammer spur. In the pics the trigger appears to be "narrow" at 0.265 width, however it could be a wider 0.400 inch smooth trigger, the pics aren't that clear on this feature on S&W's site. The barrel features an interchangeable front sight and is shipped with a gold bead Patridge sight. The action is supposed to be tuned, however any good smith can tune it to a lighter DA trigger than what it ships with. BTW, that's due to concerns of litigation, S&W has gone way heavy on triggers in the past 10 or 15 years. IMO you can expect a 10-10.5 lbs. DA trigger from the factory for a 625 PC. Ships with a gaudy red, white, and blue laminated grip that feature exactly the same profile of the wood grip on the 625 JM. The cylinder is supposed to be chamfered, however there has been one report of a 625 PC being shipped without a chamfered cylinder recently. Finish is Satin Stainless, or a "brushed" finish.

625 JM. Features an ECM rifled barrel with a full lug "heavy" profile. This barrel also features the interchangeable front sight and also ships with a gold bead Patridge sight. Personally I avoid shooting lead bullets in any S&W with an ECM barrel, tried it once and it created a mess of leading. Features flash chromed Forged hammer and trigger. The hammer is a standard "service" width hammer and the trigger is a narrow serrated trigger. Note on the serrated trigger, it's been well described as a DNA sampling device because the serrations are razor sharp. If you choose this model you can absolutely plan on pulling the trigger and grinding the serrations down with a sanding drum on a Dremel because just 50 rounds of DA shooting will leave your finger bleeding. Trigger weight is also set on the heavy side, mine measured at 11.5 lbs. out of the box. The cylinder on this version is NOT chamfered, however I was suprized to note that the extractor WAS chamfered. That made it very easy to use the chamfer on the extractor as a guide to chamfer the cylinder. The grip is a wood JM grip with the same profile of the laminated grip featured on the 625 PD. Finish is Matte Stainless, which is a rather nice looking bead blasted finish. On an odd note the Matte finish has proven to be VERY easy to clean, something I did not expect. Fact is that it's actually easier to clean than a satin finsh.

Personally, I'm a Tinkerer, so I chose the 625 JM. The wood grip is in storage and my preferred grip, the 500 Magnum monogrip is mounted on it. The trigger has been tuned to 8 lbs. DA and 3 lbs. SA. It's also had a 0.510 inch long, extended travel, Cylinder & Slide firing pin installed and ignition is 100% perfect with or without moon clips. I've also ground and polished the trigger to remove most of the serrations. I've also chamfered the cylinder and fresh clips now just fall in place. At some point in the next month or two I'll pull the barrel and lap the forcing cone, put an 18 degree crown on the barrel and hand lap the crown with valve lapping compound to match the finish on the gun. Like I said, I like to tinker.