The 'adjusting sleeve' is what is used to take up wear on the bbl/frame TD assembly. It has the 'teeth' that lock into the small key that slides in the slot.
This is the sleeve that is fine threaded onto the breech end of the bbl.
The Chamber Ring is the round approx 1/4" think sleeve that fits into the face of the recv'r and is held in with a set screw.
The bolt chambers the hull against the breech face end. That's your headspace, the space betw the closed & locked bolt face and the chamber ring.
The 'adjustment sleeve' bears against the muzzle side of the chamber ring when the bbl assembly is turned into place. That makes for a solid assembly.
You also have to figure the thickness of the chamber ring when measureing the chamber length. Add this to what the depth measurement is from the bbl itself.
More than a few thought to be short chambered guns have been made into 3" guns because of it.
When the TD gets loose, the adjusting sleeve is backed out a tooth or two so the breech again bears on the chamber ring with some force to tighten things up.
The adjusting sleeves were orig offered from the factory in 5 (maybe 6) continuing sizes to keep the assembly tight. The threads that screw them onto the bbl itself are timed a few degrees
difference so they take up quicker and tighten the TD.
Old parts lists show them at the very end of the parts lists usually. Any sleeve over the factory original fit #1 or 'A' size is hard to find these days and gets very pricey.
Same deal for the Model 42.
Adj Sleeve
Chamber Ring