zeitgenössisch
contemporary
Refers to the present era or time. It describes something that comes from today's time or is characteristic of it.
Das Museum stellt vor allem zeitgenössische Kunst aus.
The museum mainly exhibits contemporary art.

contemporary
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contemporary
Refers to the present era or time. It describes something that comes from today's time or is characteristic of it.
Das Museum stellt vor allem zeitgenössische Kunst aus.
The museum mainly exhibits contemporary art.

The word consists of 'Zeit' (time) and 'Genosse' (comrade). A 'Genosse' is a comrade or a person who belongs to the same group or time. So 'zeitgenössisch' literally means 'belonging to the same time'.
Die Ausstellung zeigt Werke von Picasso und anderen zeitgenössischen Künstlern.
The exhibition shows works by Picasso and other contemporary artists.
The meaning depends on the context. Without a historical reference, 'zeitgenössisch' means the present day. If a person or era from the past is mentioned, it means 'coming from the same time'.
Ich interessiere mich sehr für zeitgenössische Architektur. (heutige Architektur)
I am very interested in contemporary architecture. (today's architecture)
In the meaning 'from today's time', the word is very often used in cultural contexts. Common combinations are 'zeitgenössische Kunst' (contemporary art), 'zeitgenössische Literatur' (contemporary literature), or 'zeitgenössische Musik' (contemporary music).
Dieses Museum für zeitgenössische Kunst wurde erst letztes Jahr eröffnet.
This museum of contemporary art opened only last year.
simultaneously / at the same time
'gleichzeitig' and 'zeitgenössisch' both have to do with time, but in very different ways. 'gleichzeitig' describes two things happening at the same moment or at the same time. 'zeitgenössisch' describes people, works, or things that exist in the same era or come from the same period. This is usually a larger historical period, not a single moment. The words can be confused because both express closeness in time. For everyday actions, use 'gleichzeitig'. For art, history, or eras, 'zeitgenössisch' fits.

Im Museum haben wir zeitgenössische Bilder aus der Zeit des Dichters gesehen.
At the museum, we saw contemporary paintings from the poet's time.
Morgen kommen wir gleichzeitig am Bahnhof an.
Tomorrow we will arrive at the train station at the same time.