What are the two meanings of Berechtigung, and what are rights (Rechte)?

Berechtigung means either the act of authorising, or the set of rules that define when and under which conditions a subject may access a relying party's resources; rights are the abstract properties a subject must possess to be allowed access, often laid down in laws or contracts.

The distinction keeps three layers apart: rights (what you are entitled to, legally), Berechtigungen (the rules configured in the system) and authorisation (the runtime decision applying them).