der Anspruch
claim
A legally or morally justified right or claim to something.
Nach einem Jahr Beitragszahlung hat man Anspruch auf Arbeitslosengeld.
After one year of paying contributions, you have a claim to unemployment benefits.

claim / demand
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claim
A legally or morally justified right or claim to something.
Nach einem Jahr Beitragszahlung hat man Anspruch auf Arbeitslosengeld.
After one year of paying contributions, you have a claim to unemployment benefits.

'Der Anspruch' (claim/demand) belongs to the word family of 'sprechen' (to speak). The related verb 'beanspruchen' means 'to claim something for oneself' and helps you understand the idea of a right or demand.
Niemand kann diesen Erfolg für sich allein beanspruchen.
No one can claim this success for themselves alone.
A right or claim is almost always expressed with the fixed structure 'Anspruch auf etwas haben' (to have a claim/right to something). The thing one has a claim to is in the accusative.
Arbeitnehmer haben Anspruch auf bezahlten Urlaub.
Employees have a right to paid vacation.
If 'Anspruch' appears with 'auf' and the accusative, it usually means a claim or demand (m01). If it is described with adjectives like 'hoch' (high), 'künstlerisch' (artistic), or 'persönlich' (personal), it is about the level or expectations (m02).
Sie hat einen gesetzlichen Anspruch auf die Dokumente.
She has a legal claim to the documents.
This meaning occurs only in the fixed expression 'etwas in Anspruch nehmen' (to take up/use something). It means to use or claim something, for example time, help, or a service.
Die komplette Renovierung wird viel Zeit in Anspruch nehmen.
The complete renovation will take up a lot of time.
right / law
'das Recht' and 'der Anspruch' can both mean that someone is allowed to receive, do, or demand something. 'das Recht' sounds more general and can refer to something legal or moral. 'der Anspruch' puts more emphasis on the claim to something concrete, for example money, help, or a service. Learners may confuse the words because an Anspruch is often a right. When speaking generally about freedom or permission, 'Recht' fits better. When saying that someone can demand something specific, 'Anspruch' is often more precise.

Nach dem Unfall hat sie Anspruch auf Hilfe von der Versicherung.
After the accident, she has a claim to help from the insurance company.
Wir haben das Recht, unsere Meinung frei zu sagen.
We have the right to express our opinion freely.