A TIFF image with a world file displays at incorrect location in ArcMap, but displays at the correct location in ArcInfo Workstation and ArcView.
The image has GeoTIFF tags that describe a location different than the location the world file describes. ArcMap will use the information in the GeoTIFF tags if they exist, it will only use the world file if these tags are absent.
Use the ArcInfo Workstation CONVERTIMAGE command and specify TIFF as the output format. The new image will be a GeoTIFF, but the tags will describe the same location as the .tfw world file.
Arc: CONVERTIMAGE oldimage.tif newimage TIFF
For information about the GeoTIFF tags used by ArcInfo, see the ArcInfo Workstation online help: Contents > Cartography > Image Integration > Supported image formats > TIFF files.