Are you sure?
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I have already known the difference and have did researches too, I wouldn't post a thread without being sure.
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If you searched the meaning of it in business would look as so. Meaning of Staffing:
The term ‘Staffing’ relates to the recruitment, selection, development, training and compensation of the managerial personnel.
And for hiring:
The practice of finding, evaluating, and establishing a working relationship with future employees, interns, contractors or consultants .