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What's the difference of meaning between “the same…as VS. 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 a different meaning. Above examples, teachers or grammar books let us understand that the first means "the book" is not the same one but the same kind of that book; one of the same books in bookstores, and the second means the book is the very book you have.

Swan, however, explains in his book "Practical English Usage" that no difference of meaning between the same...as/that.

The same...?? the same kind....? as...? that...? I got crazy. Whose words shoud I believe? Before you, anonymous masters, give me an exact answer, I would collect my emotions.