What is the difference between the classes ArchiverTar and Archive_Tar? What is the difference between the classes ArchiverTar and Archive_Tar?  Which one is a Drupal module supposed to use?
The Archive_Tar class is a very-slightly modified version of the PEAR library Archive_Tar. ArchiverTar can be thought of as a wrapper to that library. However, depending on what your module is trying to achieve, you will probably want to call archiver_get_archiver(), since this is agnostic of the specific archive format (the system module supplies tar and zip, and your module could provide additional formats using hook_archiver_info()).