1. May I borrow this book?

- Sure. Just remember to give it back in a week.

2. May I borrow this book?
- Sure. Just remember to give it back within a week.
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In this short dialogue, does 'in' mean 'within'? Or are both different?

They both mean pretty much the same. The second one seems to carry the meaning of "the sooner, the better," but basically they're about the same.