I've tried some googling, and not having any better luck than you did. I see mention of "the choke", which would sure seem singular, yet you got two.
On the Circuit Judge, the choke is kind of slotted like, where the thread protector is smooth bore. The intent of the way the choke is made is to somewhat halt the rotation from the rifling in the barrel so you don't get quite as much of a donut pattern when shooting shot.
I've tried it with the smooth thread protector to compare. It seems to me the choke certainly helps, but I still find it donuts some. I would think it may be better with your handgun, as you don't have as long of a rifled barrel to get the wad spinning. I would be interested to hear if you see much donut effect when you try shot shells.