The PSI on the sidewall is the maximum
PSI tire can take. The only time you should inflate your tires that much is when you have over 6,520 pounds on the rear axle..IOW, only when severely overloaded.
The PSI on the Federal Certification Label on the lower doorpost behind the driver's seat is the PSI you need when loaded to the GVWR of the truck.
The PSI you should run depends on the exact size of the tire, and the load on each tire. Use a tire load/inflation table for your size tire to determine the PSI to run if you want to maximize the life of the tire.
A 2002 F350 4x2 SRW came with size LT265/75R16E tires. If you still run that size, here is the load/inflation table:
PSI max load per tire
35 . 1910
40 . 2100
45 . 2280
50 . 2470
55 . 2625
60 . 2790
65 . 3000
70 . 3105
75 . 3260
80 . 3415
Example 1: Your truck when loaded for bear weighs 4,500 on the front axle and 5,500 on the rear axle. So that's 2,250 on each front tire and 2,750 on each rear tire. Applying the above load/inflation table, you need a minimum of 40 PSI in the front tires and 60 PSI in the back tires. I'd probably pump both ends up 5 PSI more and run with 45 front and 65 rear.
Example 2: your truck when unloaded has only a driver and a toolbox and some miscellaneous junk behind the back seat and in the bed, so with a full tank of diesel it weighs 4,200 on the front axle and 3,750 on the rear axle. Or 2,100 pounds on each front tire and 1,875 on each rear tire. The table calls for a minimum of 40 PSI in the front tires and 35 in the rear. I'd probably run 45 front and 40 rear so my sweetheart could jump in with me without my having to pump up the tires.
Discount Tire has those load/inflation tables. The tire companies encourage truckers to use the load/inflation tables to get the max life out of their tires without danger of blowouts caused by underinflation. But for some reason some of the tire companies don't encourage use of the load inflation tables for pickups and vans. I guess they think we're too stupid to use the tables. Michelin doesn't even include them on their website for LT tires. They are on the MichelinTruck website for RV tires, but that doesn't include the LT265/75R16E on your truck. However, the tables apply to all brands of tires that are the same size, regardless of brand. So any load/inflation table you can find for your size tire is applicable to your Michelin tires. For example, here's the GoodYear table: