Today is Monday (28/1/2013) and "this Saturday" would mean the approaching Saturday (2/2/2013). Today is Monday (28/1/2013) and "the next Saturday" would mean the next Saturday after the approaching Saturday (9/2/2013) . BUT. Some of them may be confused and they might want to be clear. So they may say "Do you mean this Saturday or the next ... More @Wikipedia
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