Well the difference is (obvious to me), moving the file to the chest doesn't change anything in the file, it is placed in a protected area where it can do no harm.
Healing/repairing a file is the removal of the infected part (not all files can be repaired, see below), leaving a clean file in its original location.
Trojans generally can't be repaired (either by the VRDB or avast virus cleaner), because the entire content of the file is malware, so it is either move to chest or delete, move to the chest being the best option (first do no harm). When a file is in the chest it can't do any harm and you can investigate the infected warning.
The VRDB only protects certain files, mainly .exe files, it doesn't protect data files or all files, it is not a back-up program, so there are going to be many occasions where repair won't be an option.
Only true virus infection can be repaired, e.g. when a virus infects a file it adds a small part to it, provided that file is one that avast's VRDB would monitor and you have run the VRDB, then it may be possible to repair the file to its uninfected state.
However, for the most part so called viruses, trojans (adware/spyware/malware, etc.) can't be repaired because the complete content of the file is malicious.