
herausgeben
to hand over
To hand something that one owns or is holding over to another person, often in response to a request or demand.
Der Dieb wurde gezwungen, das gestohlene Geld herauszugeben.
The thief was forced to hand over the stolen money.
to hand over / publish / give change
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to hand over
To hand something that one owns or is holding over to another person, often in response to a request or demand.
Der Dieb wurde gezwungen, das gestohlene Geld herauszugeben.
The thief was forced to hand over the stolen money.

to publish
To publish a book, magazine, or other medium and make it available to the public.
Der Verlag wird im Herbst den neuen Roman des Autors herausgeben.
The publishing house will publish the author's new novel in the fall.

to give change
To give back change when someone has paid with a larger amount of money.
Können Sie mir auf 50 Euro herausgeben?
Can you give me change for 50 euros?
'Herausgeben' (to hand over / publish / give change) is a separable verb. The prefix 'heraus' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Verkäufer gibt mir das Wechselgeld heraus.
The salesperson gives me the change.
The verb consists of the directional particle 'heraus' (out of something toward the speaker) and the verb 'geben' (to give). Its literal meaning is therefore 'to give outward'.
Bitte gib den Ball aus dem Haus heraus.
Please give the ball out of the house.
In the meaning 'aushändigen' (to hand over), 'herausgeben' is often used in the context of a demand or compulsion. Typical objects are things that someone is hiding or does not give up voluntarily.
Die Polizei forderte den Verdächtigen auf, seine Waffe herauszugeben.
The police ordered the suspect to hand over his weapon.
When it is about publishing, the objects are typically media such as 'ein Buch' (a book), 'eine Zeitschrift' (a magazine), 'ein Album' (an album), or 'ein Magazin' (a magazine). The person who does this is 'der Herausgeber' (the publisher/editor).
Nächstes Jahr gibt die Band ihr neues Album heraus.
Next year, the band is publishing its new album.
To ask for change, you use the fixed structure 'auf [Betrag] herausgeben' (to give change for [amount]). The verb often appears in a question with 'können' (can).
Entschuldigung, können Sie auf einen 20-Euro-Schein herausgeben?
Excuse me, can you give change for a 20-euro bill?
to publish
Veröffentlichen and herausgeben can both mean making a work publicly available. Veröffentlichen emphasizes the process of making it accessible. Herausgeben focuses more on the role of a publishing house or responsible person who brings the work out for the public.

Der Verlag gibt den neuen Sammelband heute heraus.
The publishing house is bringing out the new anthology today.
Die Autorin veröffentlicht den neuen Sammelband heute online.
The author is publishing the new anthology online today.