
die Schuld
blame / responsibility
Responsibility for a mistake, misfortune, or wrongful action; fault.
Die Polizei untersucht, wer die Schuld an dem Unfall hat.
The police are investigating who is to blame for the accident.
guilt / debt
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blame / responsibility
Responsibility for a mistake, misfortune, or wrongful action; fault.
Die Polizei untersucht, wer die Schuld an dem Unfall hat.
The police are investigating who is to blame for the accident.

to be to blame for
To be the cause of something negative.
Ein technischer Defekt war schuld an dem Zugausfall.
A technical defect was to blame for the train cancellation.

debt
An amount of money that one owes to another person or institution. Usually used in the plural 'die Schulden' (debts).
Er hat endlich seine letzte Schuld bei der Bank beglichen.
He has finally paid off his last debt to the bank.

guilt
A moral or ethical wrongdoing; the feeling of having done something wrong.
Er fühlte eine tiefe Schuld, weil er sein Versprechen nicht gehalten hatte.
He felt deep guilt because he had not kept his promise.
'Die Schuld' (guilt/blame/debt) is part of a word family. The related verb is 'schulden' (to owe money), and the adjective is 'schuldig' (guilty; responsible for something negative).
Er schuldet mir noch 50 Euro.
He still owes me 50 euros.
Pay attention to the difference between singular and plural. 'Die Schuld' (singular) usually means responsibility, blame, or moral wrongdoing. 'Die Schulden' (plural) almost always refers to financial debts.
Er gab zu, die Schuld am Streit zu haben.
He admitted that he was to blame for the argument.
The construction 'schuld sein an etwas' (to be to blame for something) is very common. It describes the cause of a problem. The object that represents the problem is always in the dative.
Das schlechte Wetter war schuld an der Verspätung.
The bad weather was to blame for the delay.
When it is about responsibility, typical phrases are 'jemandem die Schuld geben' (to blame someone), 'die Schuld auf sich nehmen' (to take the blame), or 'Schuld haben an etwas' (to be responsible for/to be to blame for something).
Es ist nicht fair, ihm allein die Schuld zu geben.
It is not fair to blame him alone.
In a financial context, 'Schulden' (debts) is often used with verbs like 'machen' (to incur), 'haben' (to have), 'zurückzahlen' (to pay back), or 'abbezahlen' (to pay off).
Viele junge Leute machen Schulden, um studieren zu können.
Many young people incur debts in order to study.
mistake / error
A Fehler is an incorrect action or decision that can lead to a bad result. Schuld, by contrast, refers to responsibility for it. So you can identify a Fehler and then clarify who is to blame for it.

Ich trage die Schuld dafür, dass die falsche Datei an den Kunden geschickt wurde.
I am responsible for the wrong file being sent to the client.
Es war ein Fehler, die Datei vor der Kontrolle an den Kunden zu schicken.
It was a mistake to send the file to the client before checking it.