There is always confusion when a Piping engineer talks to a Mechanical engineer about the Pressure to which piping is to be designed. Piping engineers are trained to design piping to ASME B31.1, B31.3 which guides the engineer to use Design Pressure, where as ASME BPV code nominates this as Maximum Allowable Working pressure.
To give reference from ASME B31.3, Section 322.6.3 Pressure Relieving Devices, it is clear that Design Pressure is same as Maximum Allowable working pressure
Pressure