the day after vs the next day

English as a Second Language English Vocabulary, Grammar and Idioms
1

Is there any difference between “the day after” and " the next day"?

2

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I see none here-- they represent the same day.
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3

To me -
The day after=After tomorrow.
Next day=Tomorrow.
Is this correct?

Thanks,
Suresh

4

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No.

I went to Tokyo on October 17th and to Yokohama the day after.
I went to Tokyo on October 17th and to Yokohama the next day.
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