verzweifelt
desperate
Describes a person who has no hope left and no longer knows what to do.
Nachdem er seinen Job verloren hatte, war er völlig verzweifelt.
After he had lost his job, he was completely desperate.

desperate
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desperate
Describes a person who has no hope left and no longer knows what to do.
Nachdem er seinen Job verloren hatte, war er völlig verzweifelt.
After he had lost his job, he was completely desperate.

The word 'verzweifelt' (desperate) is derived from the verb 'verzweifeln' (to despair), which in turn comes from the noun 'der Zweifel' (doubt). So it describes a state in which you are overwhelmed by doubts and no longer see a solution.
Aus reiner Verzweiflung rief sie die Polizei an.
Out of sheer desperation, she called the police.
'Verzweifelt' (desperate/desperately) can describe a person (adjective) or the manner of an action (adverb). Pay attention to its position in the sentence: before a noun or after 'sein' (to be), it describes a person; with a verb, it describes the action.
Ein verzweifelter Vater bat im Fernsehen um Hilfe.
A desperate father asked for help on television.
When 'verzweifelt' (desperately) describes an action, it often appears with verbs that express effort or searching. Common combinations are: 'verzweifelt suchen' (to search desperately), 'verzweifelt versuchen' (to try desperately), 'verzweifelt rufen' (to call desperately), or 'verzweifelt kämpfen' (to fight desperately).
Die Rettungskräfte kämpften verzweifelt gegen die Fluten.
The rescue workers fought desperately against the floods.
critical
'kritisch' and 'verzweifelt' can both show that a situation is very serious or bad. 'kritisch' describes a dangerous or decisive situation in a more objective way. 'verzweifelt' emphasizes hopelessness more strongly: a person no longer knows what to do, or a situation seems hopeless. So you can still analyze a critical situation calmly, but a desperate person is under strong emotional strain. The words are easy to confuse because both sound negative. 'kritisch' fits more with danger and decision, while 'verzweifelt' fits more with a lack of hope.

Nach dem Gespräch waren die Eltern verzweifelt, weil sie keine Lösung sahen.
After the conversation, the parents were desperate because they saw no solution.
Die Lage im Krankenhaus bleibt kritisch, weil noch Personal fehlt.
The situation in the hospital remains critical because there is still a shortage of staff.