
öffentlich
public
Accessible, visible, or usable for everyone; not private.
Dies ist ein öffentlicher Park, in dem jeder spazieren gehen darf.
This is a public park where everyone is allowed to go for a walk.
public
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public
Accessible, visible, or usable for everyone; not private.
Dies ist ein öffentlicher Park, in dem jeder spazieren gehen darf.
This is a public park where everyone is allowed to go for a walk.

public
Relating to the state, the government, or the general community.
Die Regierung investiert viel Geld in öffentliche Projekte wie Schulen und Krankenhäuser.
The government invests a lot of money in public projects such as schools and hospitals.

publicly
Taking place in front of other people or in public, so that everyone can notice it.
Der Politiker hat sich öffentlich für seine Aussage entschuldigt.
The politician publicly apologized for his statement.
'Öffentlich' (public/publicly) can stand before a noun as an adjective or function as an adverb that describes a verb. As an adjective, it is declined; as an adverb, it remains unchanged.
Das ist ein öffentlicher Garten.
That is a public garden.
In the meaning 'accessible to everyone', 'öffentlich' (public) is often found in fixed combinations such as 'öffentliche Verkehrsmittel' (public transportation: buses, trains), 'öffentliche Plätze' (public squares/places), or 'öffentliche Gebäude' (public buildings).
In der Stadt nutze ich meistens die öffentlichen Verkehrsmittel.
In the city, I mostly use public transportation.
When 'öffentlich' (public) refers to the state, it often appears with words such as 'der öffentliche Dienst' (public service / work for the state), 'öffentliche Gelder' (public funds / tax money), or 'die öffentliche Hand' (the public sector / the state as an institution).
Viele meiner Freunde arbeiten im öffentlichen Dienst.
Many of my friends work in the public service.
In the meaning 'in front of everyone', 'öffentlich' (publicly) is almost always used as an adverb. It then describes verbs of speaking or showing, e.g. 'öffentlich zugeben' (to publicly admit), 'öffentlich kritisieren' (to publicly criticize), or 'sich öffentlich zeigen' (to appear in public).
Der Star hat sich nach dem Skandal lange nicht öffentlich geäußert.
The star did not comment publicly for a long time after the scandal.
open
Offen and öffentlich can both mean that people from outside are allowed to attend. Offen particularly emphasizes access without personal restrictions. Öffentlich highlights the contrast with a private or closed event.

Die Sitzung des Gemeinderats ist öffentlich, deshalb dürfen Besucher zuhören.
The town council meeting is public, so visitors are allowed to listen.
Die Gesprächsrunde ist für alle Interessierten offen, auch ohne Anmeldung.
The discussion group is open to everyone interested, even without registration.