I think your confusing property ownership to property management ie: BLM/Forest Circus
As Freddie stated, on private property, you own the ground, it is yours, you may or may not own the mineral rights below ground.
A "patented" claim, is the same, someone owns the property and the mineral rights and can do as they wish within the jurisdiction.
A private party cant claim mineral rights on private property, in this case, one would seek permission from the land owner to prospect.
Kinda like the Friday night Gold Rush boys, most lease claims for some sort of percentage
ON the other hand, public lands managed by BLM, Forest Circus in most cases can be claimed by private people, giving them rights to minerals that may or may not be in the ground.
You dont own the land, cant build on it, the only thing a mineral claim gives you rights to are the minerals in the ground, not water rights, cant keep people off your claim except if they are mining minerals, they can camp, fish, picnic, run naked through the cacti if they wish, swim, many rules and regs
This would be considered a "placer" claim.
Under ground tunneling, blasting, rock removal would be a "hard rock" or "load" claim. Whole different set of rules and regs.
One can file a placer claim over a load claim on the same property.
In most cases, GPAA does not own the claims, they belong to others that have agreements with GPAA to use.
The claim owner can dictate what or what doesn't happen on their claims relating to mining
Hope this helps clear up some of the confusion.