中・内

About

Both 中なか and 内うち (often read with onyomi 内ない if the second character in a compound) can be used to express "inside", but differ slightly in both usage and meaning.

中なか tends to mean "inside" of something (e.g. "The ball is inside the bag"):

E.g. ボールはカバンの中なかにある。
"The ball is inside the bag."

Whereas 内うち refers to "the inside" of something and is often paired with 側がわ to form the compound 内側うちがわ:

E.g. カバンの内側うちがわが汚よごれている。
"The inside of the bag is dirty."

There are some situations where both 内うち and 中なか may be used, but each word will change the nuance of the sentence.

Summary

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  中なか means "inside" while 内うち means "the inside (of something)"

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  内うち is often combined with 側がわ to form 内側うちがわ