There is a big thread on this topic here:
https://www.thorforums.com/forums/f1...ems-23626.html
Both the LT and C type tires are 10-ply E load rated tires. However, the standard LT tires are 115/112 rated and the C type are 120/121, so they have a higher load rating even though they are both classified as load range E. ( By C type I mean commercial truck tires, not load range C.) The LT tires are usually designated as LT225/75R16 and the commercial type are 225/75R16C.
I have a 2018 Chateau 31E so very similar to your 31W. It is very heavy at the rear, and I have had a few rear tire failures. Earlier this year I replaced the rear tires with General Grabber HD tires, 225/75R16C, with the load index 121/120. We are doing a 6500 mile trip starting in a couple of weeks and hopefully won't have any tire issues.