Physicist here. Classical error correction may not always be a straight up repetition code, but the concept of redundancy of information still applies (like parity checks).

In a nutshell, in quantum error correction you cannot use redundancy because of the no-cloning theorem, so instead you embed the qubit subspace in a larger space (using more qubits) such that when correctable errors happen the embedded subspace moves to a different "location" in the larger space. When this happens it can be detected and the subspace can be brought back without affecting the states within the subspace, so the quantum information is preserved.