Is there a difference in the ruling regarding atonement between intentional homicide that mandates Qisas and intentional homicide that does not?

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There is no difference; the ruling applies equally whether the intentional homicide mandates retribution (Qisas) or does not. This includes cases such as a father killing his son, a master killing his slave, a free person killing a slave, or a Muslim killing a disbeliever, as these are all classified under types of intentional killing.