It could be that the homeowners have added an addition to the home since the county did a reappraisal.
Also, it is important to note that the county appraisers do not actually go inside the home to measure. They measure around the outside of the home to get the square footage measurement, which isn't always the most accurate.
Finally, the home in question states the source for sqaure footage as "Homeowner." Well, in my experience, this is not a good source for a measurement. I would take the tax records over the homeowner's word unless they can show me evidence of the remodel/addition or a legit measurement from an appraisal.
The homeowners should be able to tell you why there is a discrepancy. Where did they get that number?