Two major types of water hardness?

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Hardness is caused by dissolved calcium and magnesium ions, and it’s useful to classify it by the chemical forms of those salts. Carbonate hardness represents the presence of carbonate and bicarbonate salts of calcium and magnesium. Noncarbonate hardness covers all the other salts (such as sulfates and chlorides) of those same ions. Boiling removes carbonate hardness because calcium carbonate precipitates out, which is why that portion is called temporary. The noncarbonate portion doesn’t precipitate with heating, so it remains—hence permanent hardness.

Naming the two major types as carbonate and noncarbonate directly reflects these chemical categories, making it the best way to describe the two principal forms of hardness. (Temporary vs permanent is another common label for the same distinction, but the carbonate/noncarbonate pairing aligns with the underlying chemistry.)