release / publication
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release / handover
The act of handing over or returning something that is demanded or belongs to someone else.
Die Entführer forderten Lösegeld für die Herausgabe der Geisel.
The kidnappers demanded ransom for the release of the hostage.
'Herausgabe' is the noun formed from the separable verb 'herausgeben' (to hand over / to publish). It describes the act of 'Herausgeben' (handing over / publishing).
Er weigerte sich, die Schlüssel herauszugeben.
He refused to hand over the keys.
If the context is books, newspapers, or music, 'Herausgabe' means publication. If the context is objects, data, or people, it means handover, surrender, or return.
Die Herausgabe des neuen Albums wurde verschoben.
The release of the new album was postponed.
In the sense of 'Aushändigung' (handover), Herausgabe is often 'gefordert' (demanded), 'verlangt' (requested/demanded), or 'verweigert' (refused). This usage is common in formal or legal contexts.
Der Anwalt forderte die sofortige Herausgabe der Dokumente.
The lawyer demanded the immediate handover of the documents.
In the sense of 'Veröffentlichung' (publication), someone is often 'für die Herausgabe verantwortlich' (responsible for the publication) or works 'an der Herausgabe mit' (contributes to the publication).
Professor Müller ist für die Herausgabe dieser Fachzeitschrift verantwortlich.
Professor Müller is responsible for the publication of this academic journal.
expense / issue / output
'die Ausgabe' and 'die Herausgabe' can both have to do with giving or publishing. With books or magazines, 'Ausgabe' usually means the specific issue or edition that you can read. 'Herausgabe' more often means the process or responsibility of publishing a work. In addition, 'Herausgabe' can mean that something must be returned or handed over, for example documents. 'Ausgabe' is more suitable for the distribution of things or for a specific publication. The risk of confusion comes from the fact that both words come from 'geben' (to give). The important point is: 'Ausgabe' is often the result or the distribution, while 'Herausgabe' is the act of publishing or returning something.
Die Herausgabe der alten Briefe wurde vor Gericht gefordert.
The handover of the old letters was demanded in court.
Die aktuelle Ausgabe der Zeitschrift liegt schon im Kiosk.
The current issue of the magazine is already at the newsstand.