A world file stores an affine or first order transformation that maps from pixel space to map space. When an image is georeferenced and the transformation can be expressed in the form of a world file, Update Georeference creates a world file.
Since ArcGIS 9.2 Service Pack 2, if the transformation cannot be expressed as a world file, Update Georeference writes the transformation into the aux.xml file and also writes an approximate affine transformation into a text file or a world file with an 'x' on the end of the extension name. For example, a TIFF image with this approximate affine transformation has the extension .tfwx. This is not an exact transformation; it is only an approximation.
There is a special case where this text file contains a true affine transformation. If performing Update Georeference on a raster dataset that already contains map coordinates, a text file with the 'x' extension is written. For example, if georeferencing is performed on a TIFF that already contains map coordinates, the Update Georeference command creates a .tfwx file that contains a true affine transformation.
This text file can be used as a world file if it is needed for ArcGIS 9.1 and non-ArcGIS software. To use this text file, delete the 'x' in the world file extension name. Since this text file is not a part of the raster dataset in ArcGIS 9.2 and later versions, it should not be used as a world file in versions where ArcGIS can read the aux.xml file, such as in ArcGIS 9.2 and beyond.