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Usually, the term 'story' has much to do with habitable space, and not attic, or unused space. The definition and regulations for or against stories above a certain number come from the fire department, insurance, and life/safety concerns based on available local fire fighting abilities and equipment. In that case, the 'attic' or uninhabited space above your neighbors second floor space would not constitute a third story. But if the word 'story' is defined in terms of building height, your neighbor may have an issue with it.
Bottom line is, don't depend on a strict definition or yes/no answer to your question here. Look into your local development covenants (if they exist) or your local zoning code for the answer.