Why the Coulombic pairwise energy is so different for two kinds of rigid water implementations- fix shake and fix rigid

Dear Steve,
Thanks you very much.
Yes, the special bonds result in the difference. Now I can obtain the same potential energy for these two models if I set bonds and angles in fix rigid model.
Also I noticed that the fix rigid changes the potential energy, and whether this change can be add to the thermo output or not by using fix_modify energy option.