The thread difference is all the older HK, and early Benelli USA models have the thread at the very end of the barrel. Those are called Mobil chokes and they are maybe 1" or a little more. All new ones for quite a while, I am guessing around 2002 maybe, have Crio chokes. Those are longer maybe around 1.5" and the threads are maybe 3/4" down inside the barrel. They are about the same length as many extended chokes in the Mobil style, but it all fits inside the barrel.
You can do a search on the threads here and find who does the threading, cost, limitations, etc. But, for a quick recap I'll tell you that some barrels are either too thin, or they have to run another choke type that is thinner such as Rem-Choke's. Briley is who is most often recommended if I remember right for the cutting and threading. They'll keep everything legal too and make sure you don't go too short where you'll need to register it as a Short Barrelled Shotgun (SBS). If that is actually what you are after, I am not positive they do that, but they might.