Hi Juan. Despair simply means hopelessness. Desperation is a reckless, violent condition caused by despair. Examples: He was full of despair because his mother had died. He robbed the bank, out of sheer desperation in order to pay back his gambling debts.

They are both nouns. Desparation is the felling of being desparate. You'd do almost anything for someyhing. Despair is the felling of hopelessness or uselessness.