Kosher salt refers to a salt that is crystallized under pressure to produce larger flat flakes of salt. It does not have less sodium per gram than any other salt. However, because of the crystal shape difference, it would have less sodium per teaspoon than, say, table salt (much smaller grains - thus more densely packed). Weight to weight it would be the same.
Kosher salt is pure sodium chloride and does not have iodine added to it.
Sea salt, as it sounds, is made from dehydrating sea water. Because it is not crystalized pure it contains many other minerals and potential nutrients from the sea water. Sea salts from different parts of the world will have different mineral contents. Sea salts can add different depths of flavor besides just the saltiness.
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