die Forderung
demand
An emphatic wish or demand that someone makes.
Die Hauptforderung der Streikenden ist eine Lohnerhöhung um fünf Prozent.
The main demand of the strikers is a five-percent pay raise.

demand / claim
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demand
An emphatic wish or demand that someone makes.
Die Hauptforderung der Streikenden ist eine Lohnerhöhung um fünf Prozent.
The main demand of the strikers is a five-percent pay raise.

'Die Forderung' (the demand/claim) is derived directly from the verb 'fordern' (to demand). The ending '-ung' turns the action of demanding into a noun.
Die Mitarbeiter fordern mehr Lohn, und ihre Forderung ist berechtigt.
The employees are demanding higher wages, and their demand is justified.
In connection with wishes or demands, a 'Forderung' (demand) is often 'gestellt' (made) or 'erhoben' (raised). When someone meets the demand, the 'Forderung' is 'erfüllt' (fulfilled).
Die Gewerkschaft hat die Forderung nach kürzeren Arbeitszeiten gestellt.
The union has made the demand for shorter working hours.
When describing exactly what is being demanded, German usually uses the preposition 'nach' followed by the dative.
Die Forderung nach mehr Transparenz wurde immer lauter.
The demand for more transparency grew louder and louder.
In a business or legal context, 'Forderung' (claim) almost always refers to a claim to money. Typical verbs here are 'eine Forderung begleichen' (to settle/pay a claim) or 'eine Forderung eintreiben' (to actively collect money owed).
Die Rechnung ist überfällig, wir müssen die offene Forderung nun eintreiben.
The invoice is overdue; we now have to collect the outstanding claim.
guilt / debt
'Schuld' and 'Forderung' are on two different sides in the area of money. A debt is money that you have to pay someone; in German, people usually say 'Schulden' (debts) here. A 'Forderung' is the claim that someone has to pay you money. Learners may confuse the words because both have to do with outstanding payments. The simple difference is: the person who has to pay has debts. The person who is entitled to receive money has a claim.

Die Firma schickt dem Kunden eine Forderung über 300 Euro.
The company sends the customer a claim for 300 euros.
Nach dem Umzug hatte Paul noch Schulden bei der Bank.
After the move, Paul still had debts with the bank.