For Fastback, it's generally a backup tools targeting for workstation utilizing the snapshot technology for fast recovery.
For Flashcopy manager, it's targeted for use with SAN level (for IBM product term, it's flashcopy) and could have scheduled automation for backing up the flashcopy lun onto TSM if such environment available in the infrastructure.
You may also see flashcopy manager used in new version of TDPO (sql for example) to backup the SQL database from an flashcopied copies to TSM, it's just like the old days which use VSS, but more SAN related technology.