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Temporal steering and violation of the Leggett-Garg inequality are twodifferent ways of probing the violation of macro-realistic assumptions inquantum mechanics. It is shown here that under unitary evolution and projectivemeasurements the two types of temporal correlations lead to similar results.However, their inequivalence may be exhibited if either one of them is relaxed,i.e., by employing either generalized measurements, or noisy evolution, as weshow here using relevant examples.

Probing hierarchy of temporal correlation requires either generalised measurement or nonunitary evolution