The difference between batch stamping and batch publishing is that when the latter is performed, no stamp is applied. When performing a batch publish, the batch stamp template selected (or the settings selected on the Advanced tab) should have no stamp template selected. Copies of the selected files are published into destination folder with the characteristics specified in the other indicated settings.
File History - the batch stamping or publishing
event displays in the history for the original file only. The resulting
stamped files only show upload information.