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Difference between “the same…as” and “the same …that”

I have the same book as you have.

I have the same book that you have.

In Korea, we learn that the same...as and the same...that have different meanings. Teachers or grammar books say that the first example sentence means the book is not the same one but the same kind of that book or one of the same books in the bookstores, while the second means the book is the very book you have.

Swan, however, explains in his book Practical English Usage that there is no difference in meaning between the two cases.

Who is correct?