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duhh
Well apparently, distilled water is healthier for us due to the "no bacteria" factor. Boiled water can be consumed, but after the boiling process there can still be bacteria present in the water. Boiled water should only be used in an emergency situation, and when boiling water for drinking purposes the water should be boiled more than once. A better process would be to boil the water and then distill the water for better purification.
Base on the information that you wrote.