Uniform Standards of Professional Appraisal Practice
The Uniform Standards of Professional Appraisal Practice, or USPAP, are the ethical and performance standards for appraisers in the United States. They are written by the Appraisal Standards Board of The Appraisal Foundation.
USPAP requires appraisers to identify the characteristics of a property that matter to the assignment and to report them in a way that is not misleading. Size is one of those characteristics, so a clear, consistent measurement is part of doing the job right.
USPAP does not say how to measure a house. It leaves that to other sources. For loans sold to Fannie Mae the method is ANSI Z765, and the appraiser states on the report which standard was used.
Further reading: Uniform Standards of Professional Appraisal Practice on Wikipedia.