Qual è la differenza tra the next week e next week ?Sentiti libero di rispondere con un esempio.

I think the explanation you found is correct. If on Wednesday I say "I need to finish this report in the next week.", then I mean I must finish the report before next Wednesday.
But if I say, on Wednesday, "I need to finish this report next week.", then I mean I must finish the report before the end of next week.

The starting day for a week is different in different countries. Traditionally, in America, the week starts on Sunday. But sometimes people decide they want their week to start on Monday.

"Next Sunday" is not different from "Sunday next week".

I hope this helps!