despair the feeling that everything is wrong and nothing will turn out well; "they moaned in despair and dismay"; "one harsh word would send her into the depths of despair"
A resignation is the formal act of giving up or quitting one's office or position. It can also refer to the act of admitting defeat in a game like chess, indicated by the resigning player declaring "I resign", turning his king on its side, extending his hand, or stopping the chess clock. A resignation can occur when a person holding a position gained by election or appointment steps down, but leaving a position upon the expiration of a term is not considered resignation.
OmegaWiki Dictionary
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resignation A written or oral declaration that one resigns.
resignation The act of voluntarily quitting one's job.