die Nachricht
message
A brief piece of information that is communicated to someone orally, in writing, or electronically.
Ich habe dir eine Nachricht auf dem Handy hinterlassen.
I left you a message on your phone.

message / news
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message
A brief piece of information that is communicated to someone orally, in writing, or electronically.
Ich habe dir eine Nachricht auf dem Handy hinterlassen.
I left you a message on your phone.

Here, number is very important for the meaning. 'Eine Nachricht' (a message) in the singular is a personal message. 'Die Nachrichten' (the news) in the plural almost always means 'the news' on television, radio, or the internet.
Ich habe eine Nachricht von meiner Freundin bekommen.
I received a message from my girlfriend.
The word derives from 'nach' (after/to) and 'richten' (to direct). A 'Nachricht' (message/news item) is therefore information that is 'directed' toward someone or something, meaning it is communicated deliberately.
Bitte richte ihm aus, dass ich später komme.
Please tell him that I'll come later.
For personal messages, German uses verbs like 'eine Nachricht schreiben' (to write a message), 'senden' (to send), 'bekommen' (to receive), 'hinterlassen' (to leave), or 'überbringen' (to deliver).
Kannst du mir später eine Nachricht schicken?
Can you send me a message later?
When it comes to the news in the media, German uses verbs like 'die Nachrichten sehen' (to watch the news), 'hören' (to listen to), 'lesen' (to read), or 'verfolgen' (to follow).
Hast du heute schon die Nachrichten gehört?
Have you already heard the news today?
information
'Information' and 'Nachricht' can both refer to something that you learn or pass on. But 'Information' is more general: it can be a fact, a piece of information, or knowledge about a topic. 'Nachricht' fits better when someone actively sends or says something to another person, for example by phone. In the media, 'die Nachrichten' means current news from around the world. Learners easily confuse the words because a message often contains information. In practical terms: the information is the content; the message is often the form in which the content arrives.

Nach der Arbeit schreibt mir mein Kollege eine kurze Nachricht.
After work, my colleague writes me a short message.
Die Information über den Zugausfall steht auf der Anzeigetafel.
The information about the train cancellation is on the display board.