A pcp will use more volume because the air is the only energy source, a break barrel has a chuffing great spring
Remember school physics ? - the amount of energy that exists in the universe is finite all we can do is change the form of that energy,
So you transfer energy (which you got from food) from your body to compress the spring, which stores that energy in the spring tension, when released the spring transfers that stored energy in to the air as both pressure, heat & recoil, the air in turn transfers the energy in to propelling the pellet which in turn transfers it to the target.
The pcp only has the energy stored within the air pressure, so no effort from you & no recoil but the pay off is more air is used per shot.
A regulator (very basically) is a valve between the main store of air in the bottle & the single shot store in the firing chamber,it uses spring & air pressure to only allow a pre-set pressure in to the firing chamber rather than the actual pressure in the bottle so the pellet always has the same pressure pushing it across the whole bottle charge.
Air is "wasted" because the pellet has to be accelerated up to the required velocity within a very short time & barrel length and the transfer system is not all that efficient due to the need for the pellet to be free to move & exit the barrel.