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What's the difference between 差 and 違い? When would I use each?

Which (if either) would I use for describing the difference between something
like sample data and the best fitting equation?
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2012-03-22T15:26:23.430
5079
2022-12-20T17:57:59.723
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kanji word-choice
What's the difference between differences? 差 and 違い
`違い` simply means "difference". `差` means difference in the sense of a margin
or gap, and seems to relate to things that are calculable.

> [誤差]{ご・さ} → Margin of error  
>  [時差]{じ・さ} → Difference in time - (時差ぼけ → Jet lag)

It seems like you could replace most instances of `違い` with `差`, but not the
other way around. `差` is definitely more appropriate when talking about sample
data, etc.

However, there might be times when the two have distinct meanings. For
example, say you have a boy who is 10 years old, and another who is 20. `年齢の差`
would be "10 years", but `年齢の違い` might describe how the characteristics of
their ages differs; like "10-year-olds have more energy, but 20-year-olds are
smarter." Not sure if this is correct, but seems different to me.
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2012-03-22T18:16:27.787
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2022-12-20T17:57:59.723
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I agree in general with istrasci's answer. Just to add, `差` is used
particularly for things whose difference is evaluated by the _difference in
the mathematical sense_ (that is, by subtracting the value of one from that of
another). Times and ages are usually compared in this way, so it it
appropriate to use `差`.

`違い` is a general term for describing differences. Difference among things
that do not have a clear quantity or things that are not evaluated by
subtraction is expressed as `違い`. Things like the difference between Picasso
and Monet's paintings, which cannot be easily quantitized, or the volume of a
sound, which is usually evaluated as magnitude rather than difference, can be
expressed as `違い`.
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2012-03-22T20:04:39.573
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2012-03-31T02:39:54.733
2012-03-31T02:39:54.733
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You can use both to denote a "difference" in a casual conversation. E.g. in
many contexts, 違いが分からない ＝ 差が分からない. If a person is really nice to your friend
and really mean to you, you could say「この（扱いの）差はなんだ……？」. Similarly you could
use 差 to describe change, e.g.「一年前との差」. In both cases, you could replace 差
with 違い if you wanted to.

The differences are as follows:

  * Only 差 can be used for [mathematical differences, as given here](https://kotobank.jp/word/%E5%B7%AE-67667) (second definition under さ) 
  * Only 違い can be used to denote [a "mistake", as given in the second definition here](https://kotobank.jp/word/%E9%81%95%E3%81%84-559087). However, note that only 差 can be used to denote a calculable "error" in a mathematical/scientific context, e.g.「誤差」= "margin of error".
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2019-05-12T13:39:43.947
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2019-05-12T13:39:43.947
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