After clipping a shapefile with the geoprocessing wizard, a new shapefile results. Zooming in on the borders of the new shapefile reveal that they do not match those of the original shapefile.
The discrepancy between the borders is a result of ArcGIS using integer space for snapping.
Solution or Workaround
Converting the data to a geodatabase and setting the appropriate spatial domain that corresponds to the desired precision eliminates the discrepancy.
To find information about setting the appropriate spatial domain, search the desktop help index with Geodatabases > Spatial Domain > Setting the appropriate geodatabase spatial domain.