In food, the energy stored in one form of molecules got released by converting the molecules by breaking it down into other molecules. That is, the energy released is stored in the bonds of atoms.
In Nuclear reaction, the energy released is stored in the binding energy that hold the nucleus(proton+neutron core). Thus the name nuclear, from nucleus. Not exactly correct, but an easy way to visualize where the energy is. Food from bond between atom, nuclear from the core of an atom.
Edit: and yeah all these energy is stored/detected as mass.
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