A Better Finder Rename offers the choice between a number of technical ways in which the actual file renaming takes place.
The default mode which is selected for you when you first launch the application is appropriate for most uses and there is usually little reason for changing this setting.
There are, however, situations in which this mechanism may not work correctly. This can be the case with third-party file systems, remote volumes and external storage devices that are not 100% compatible with macOS. In such cases, you may want to try using the other mechanisms.
This is the recommended mechanism for use with Mac OS X 10.7 Lion and later.
This was the recommended mechanism for use with Mac OS X 10.6 Snow Leopard, but can still be useful in some situations.
This uses the Carbon APIs to rename files and is compatible with international character sets.
When the current version of A Better Finder Rename encounters a problem renaming a file, it will automatically try all remaining mechanisms, so the only reason to change the default mechanism is for performance reasons.