What is the difference between the Design Coil Load (Btu/hr) and the Nominal Total Capacity (Btu/hr) reported from EnergyPlus.

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Your design coil load already includes the 15% since it comes from the zone level. This is what should matter to USGBC.

The design coil load is what happens at the sizing peak load, with the actual inlet temperatures.

The Nominal Total Capacity, or rated total capacity, is what would happen at standard (rated) conditions. It's a way to do an apple-to-apple comparison, similar to what you'll find in manufacturers' catalog.

See page 1949/1987 of the I/O reference manual (v8.2):

Equipment Summary

[...] - Cooling Coils includes the nominal total, sensible and latent capacities, the nominal sensible heat ratio, the nominal efficiency, nominal UA value, and nominal surface area for each cooling coil. These values are calculated by calling the cooling coil simulation routine with the rated inlet conditions: inlet air dry bulb temperature = 26.67C, inlet air wet bulb temperature = 19.44C, inlet chilled water temperature = 6.67C.

For more information about the simulation routine, refer to the coils sections in the engineering reference manual especially pages starting at 402/1304 and at 584/1304

The "Design" load is based on the coil entering conditions occurring during the entire Sizing process with all the design day information etc. The "Nominal" uses the coil entering conditions that are taken from standard rating conditions. The same size coil will have a different apparent capacity when subjected to different coil entering conditions.