Yes, if one is in despair he may have lost faith and hope, he is hopeless. One can be overcome by a sense of defeat, seeing no light at the end of the tunnel.
Of course at the end of a hole they say that there´s always a spring, that ejects people to higher places and new begginings!
Desperation is energized despair, vigorous in action, reckless of consequences.
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Desperation may lead to blind fury, or somehow to lead someone to fight for his life, for change, etc.
Desperation is also the state of being desperate.