What is the difference between a volume-limited-payload and a maximum-zero-fuel-weight-limited-payload?
The Maximum Zero Fuel Weight Payload, is the amount of payload $m_{pl}$ (i.e.: passengers, cargo, but not fuel) required to reach the  Maximum Zero Fuel Weight condition while keeping the fuel weight, $m_{fuel}$ to zeros so:

$$ 
while \; m_{fuel} =0: \\
MZFW = OEW + m_{pl} \\
$$

The Maximum Zero Fuel Weight ($MZFW$) is an indicator of the maximum loads that the wing structure can bear. For the wing an "unloaded" situation (no fuel in the wing) is critical, since the fuel stored in the wing helps reducing the loads on it in flight. The lift acts "upward" while fuel weight acts "downward", thus the fuel contribution helps relieving loads from the wing structure.

The volume limited payload is an indicator for the sizing of the cargo compartment structures. These are the structures of the cargo area, where the LD containers are stored (under the floor of the passenger cabin). This Volume Limited Payload is set to avoid having too "dense" LD containers, the limit of density for the containers is around 350 $kg/m^3$, you can find some technical specifications for LD container here.