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I noticed "Differenz" is the equivalent of the English word "difference", since I used "Unterschied" till now.

Are the two completely interchangeable?

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Unterschied/Unterscheidung is more like distinction: "Seine außergewöhnliche Stimme unterscheidet ihn von den anderen Teilnehmern (His extraordinary voice made the distinction between him and the others participants)" or "Die neue Gesetzgebung unterscheidet nicht zwischen Kindern und Erwachsenen. (The new law makes no distinction between adults and children)" –  Em1 Jun 2 '12 at 8:47

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up vote 14 down vote accepted

"Differenz" is strictly a mathematical term. It is the quantitative difference between two numbers:

Was ist die Differenz von 9 und 3?

Antwort: 6

whereas "Unterschied" typically means a qualitative difference, which can have more than one answer:

Was ist der Unterschied zwischen 9 und 3?

Antwort 1: 9 ist größer als 3.

Antwort 2: 3 ist eine Primzahl, 9 nicht.

Antwort 3: 9 ist eine Quadratzahl, 3 nicht.

Also note that "Differenzen", in plural, almost always means "conflicting views (of 2 or more persons) on a certain matter". I would not use it in singular in this meaning and don't think I've ever seen it used in singular this way.

Example:

Nach unserem Gespräch konnten wir unsere Differenzen beilegen.

After our talk, we could settle our differences.

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+1 for mentioning "conflicting views" which is an important meaning of the German "Differenz(en)" –  splattne Jun 2 '12 at 8:13

No, they're not interchangeable. If you say Differenz, then I think of something like 2-1, for which the English difference is also appropriate. But for

What's the difference between Unterschied and Differenz?

you should use "Was ist der Unterschied".

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"Unterschied" generally compares two subjects with each other, whereas
"Differenz" asks for a quantity to describe the distinction.

For this reason both expressions are not interexchangeable.

Here is an example where such an attempt would fail:

  • Was ist der Unterschied zwischen einem Apfel und einer Karotte? - a meaningful question
  • Was ist die Differenz zwischen einem Apfel und einer Karrotte? - ???

The latter question asks for a quantity that separates an Apple and a carrot - which does not make sense to ask when taking about objects such as food.

When using the term "Differenz", the two compared objects need to be of the same kind (or set - in mathematics).

For example, you can extend the second question and make it meaningful by referring to an attribute that they have in common:

Was ist Differenz der Gewichte von dem Apfel und der Karotte?

The compared objects are "Gewicht des Apfels" and "Gewicht der Karotte".

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Nice to see you here! Shouldn't your first question have "zwischen" as well? –  Gigili Jun 2 '12 at 11:39
    
@Gigili Of course! Thanks :) –  user1654 Jun 2 '12 at 11:40

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