Differentiate duty from responsibility

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Many people is confused the two thing; duty and responsibility. How would you define duty and responsibility? for example: Between the mother and her child, is it duty or responsibility? Between the employee and his work, is it duty or responsibility? Between the teacher and his student, is it duty or responsibility? Between the dog and its master, is it duty or responsibility? Between the father and his family, is it duty or responsibility? Mylotters help me to figure it out..... TY