GVWR is all about how the truck is registered (tagged) in your state. Depending on your state, the difference can be nothing or anything over #10,000 is considered a commercial vehicle..
Some states like my state has no GVW or ladin or tonnage or anything or use the trucks GVWR for registration purposes on a private use truck. The GVW line on all of my private use trucks registration papers are blank. We simply carry weight up to the lessor of the individual GAWRs or tire load ratings.
Now when I put a truck in commercial service pulling a trailer then my trucks are required to be registered at a GVW for declaring how much GCW I operate at.
Looks like the OP has a grasp about Fords F250/350 SRW same truck platforms and load carrying potentials.