The purpose of unhardened derivation is to allow for cases 1 and 2 to derive the same keys as each other. It works because both actually hash the same data, and that adding two scalars will result in the discrete log for the result of adding two points.
In case 1, we take the left part of the hash as a scalar, and add it to the parent private key (also a scalar). In case 2, we take the left part of the hash as a scalar, multiply it by the generator point G to get a point, and add it to the parent public key (which is the parent private key multiplied by G).
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