Floor is where you get off or live. Story is a measurement of height. You would say: I live on the 10th floor. That building is 30 stories high. You would not say: I live on the 10th story. That building is 30 floors high. An example of this is that a lot of buildings do not have a 13th floor. So the person on the 14th floor would be 13 stories ... More @Wikipedia
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