Heavy water
A water molecule contains two Hydrogen atoms and an Oxygen atom. Hydrogen has three isotopes protium (99.98%), deuterium and tritium. Deuterium has a neutron in the nucleus in addition to the electron and the proton Deuterium is as twice as heavier than the most abundant Hydrogen atom.
Heavy water contains a large proportion of deuterium atoms than the usual Hydrogen atom. Therefore, its molecular weight and the density is higher than the normal water.
Hard water
In general, water contains some amount of minerals such as Magnesium, Calcium and Potassium. But, hard water contains more minerals, especially Magnesium (Mg) and Calcium (Ca) than normal water (soft water). Due to this fact, the hardness of the hard water is greater than the hardness of the normal water.
Soft water
Soft water is treated water which contains sodium ions mostly.No other can be found much in that.Soft water sometimes has a salty taste to it and in some cases is not suitable for drinking.
So we can say that the major difference between hard water,soft water and heavy water is in their composition itself.