Two different plurals for das Wort

The German word for "word" is das Wort, as you surely already know. But had you noticed that there are two different plurals for it: die Worte and die Wörter? It's hard to know which is correct without understanding the distinction in meaning between the two possibilities. Let's take a look at some examples, starting with die Worte:

Worte sind jetzt fehl am Platz...

Words now are out of place...

Caption 26, Florian Bronk: Du und ich
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Und Worte können das nicht ändern, nein.

And words cannot change that, no.

Caption 22, Luxuslärm: Einmal im Leben
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So, liebe Anja, vielen, vielen Dank für deine netten Worte.

So, dear Anja, thanks very, very much for your kind words.

Caption 62, Anja Polzer; Interview
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Flüchtlinge können bei ihrer Ankunft oft nur wenige Worte oder gar kein Deutsch.

Refugees can, upon their arrival, often speak only a few words of German or none at all.

Caption 3, Flüchtlingskrise: Deutschkurse für Flüchtlinge
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And moving on to die Wörter:

Kennt ihr diese kleinen Wörter?

Do you know these little words?

Caption 4, Deutsch mit Eylin: Pronomen
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Nun kennt ihr also die Wörter für die wichtigsten Farben.

So now you know the words for the most important colors.

Caption 40, Eva erklärt: Farben
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Hierfür werden dir einige Wörter vorgeschlagen.

For this, several words will be suggested to you.

Caption 40, German Intro: Cettina
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Hier, ein Notizbuch für alle neuen Wörter auf Deutsch.

Here, a notebook for all of the new German words.

Caption 14, Nicos Weg: Wo ist der Bahnhof?
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As you may have noticed above, die Wörter is usually used in a context of learning German and relating to a specific word—to the words themselves as such: Fremdwörter, Lieblingswörter, Modewörter, Passwörter, and Reimwörter are some compound word examples.

Die Worte, on the other hand, is talking about the context of words in terms of quotations, ways of speaking, or entire topics: Bibleworte, Ehrenworte, Grußworte, Nachworte, and Zauberworte, for instance.

A few words even allow for both types of plurals. For instance, if you are making a list of keywords for a website, you'd use Stichwörter. But if you are talking generally about keywords in the more abstract sense of concepts or guiding principles, you'd use Stichworte.

Further Learning
Try and guess the meaning of the compound words listed above that use das Wort as their root, and then check your dictionary to see if you got it right. You can then go to German Yabla and find other examples of the words discussed above to see them used in a real world context.

If you're feeling extra brave, you can read the (as always) brilliant article by Der Spiegel author Bastian Sick about Worte vs. Wörter. As he so cleverly puts it: Wörter bestehen aus Buchstaben, Worte aus Gedanken.