I think what CSP means is lay the old and new ring gears, (aka crown gear ) on a flat surface and measure the height of both. The easiest way to do this is to lay a flat bar across the teeth, and measure from the flat surface to the bottom of the bar.
My wag is one of the ring gears is thicker, and it's the one with 39 teeth on the ring gear.
The correct term is the carrier, ie, " I bolted the ring gear to the carrier"
1957 WILLYS pickup,
1973 J 4000,
1978 CJ7 DD.
1979 CJ7 360, TH400/Quadratrac.
1980 CJ5 trail Jeep.
1989 YJ the CJ to YJ.