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Zeitung vs. Zeitschrift vs. Magazin

While the German words Zeitung, Zeitschrift, and Magazin all refer to published periodicals, they are not interchangeable. Each word carries a specific meaning related to its frequency of publication, content, and format, much like the difference between a newspaper and a magazine in English.

Zeitung

A1
This is the direct German word for newspaper. A Zeitung is typically published daily or weekly and focuses on current events, politics, sports, and local news. It is usually printed in a large format on inexpensive newsprint paper.
Ich lese jeden Morgen die Nachrichten in der Zeitung.
(I read the news in the newspaper every morning.)
Die Lokalzeitung berichtet über das Stadtfest am Wochenende.
(The local newspaper is reporting on the city festival this weekend.)
Kannst du den Sportteil aus der Zeitung für mich aufheben?
(Can you save the sports section from the newspaper for me?)
Er hat eine Anzeige in die Sonntagszeitung gesetzt.
(He placed an ad in the Sunday newspaper.)

Zeitschrift

A2
This is the general term for magazine or journal. A Zeitschrift is published less frequently than a newspaper (e.g., weekly, monthly, or quarterly) and covers specific topics or interests in greater depth. This term is broad and can refer to everything from a hobby magazine to a serious academic journal. They are usually printed on higher-quality, glossy paper.
Er hat einen Artikel in einer wissenschaftlichen Zeitschrift veröffentlicht.
(He published an article in a scientific journal.)
Ich habe ein Abonnement für eine Zeitschrift über Fotografie.
(I have a subscription to a magazine about photography.)
Im Wartezimmer des Arztes liegen immer viele alte Zeitschriften.
(There are always many old magazines in the doctor's waiting room.)
Diese Fachzeitschrift für Architekten ist sehr teuer.
(This trade journal for architects is very expensive.)

Magazin

B1
This word is very close in meaning to Zeitschrift and is often used for popular, consumer-oriented magazines. A Magazin typically implies a modern, visually-driven publication with a mix of articles, interviews, and many colorful photos. It is the preferred term for lifestyle, fashion, gossip, or popular news magazines. Essentially, every Magazin is a type of Zeitschrift, but not every Zeitschrift (like a dry academic one) would be called a Magazin.
Der Spiegel ist ein bekanntes deutsches Nachrichtenmagazin.
(Der Spiegel is a well-known German news magazine.)
Sie blättert in einem Hochglanzmagazin, um sich über die neueste Mode zu informieren.
(She is flipping through a glossy magazine to find out about the latest fashion.)
Das Reisemagazin hat einen Bericht über die schönsten Strände Europas.
(The travel magazine has a report on the most beautiful beaches in Europe.)
Dieses Automagazin testet die neuesten Elektromodelle.
(This car magazine is testing the newest electric models.)

Summary

In short, use Zeitung specifically for a newspaper. Use Zeitschrift as the general, all-purpose term for any magazine or journal, especially for specialized or academic publications. Use Magazin for popular, glossy, and visually-focused consumer magazines, which are a specific subtype of Zeitschrift.