Backup files can be made by copying the old file or by renaming it. This makes a difference when the old file has multiple names. If the old file is renamed into the backup file, then the alternate names become names for the backup file. If the old file is copied instead, then the alternate names remain names for the file that you are editing, and the contents accessed by those names will be the new contents.
The method of making a backup file may also affect the file's owner and group. If copying is used, these do not change. If renaming is used, you become the file's owner, and the file's group becomes the default (different operating systems have different defaults for the group).
Having the owner change is usually a good idea, because then the owner
always shows who last edited the file. Also, the owners of the backups
show who produced those versions. Occasionally there is a file whose
owner should not change; it is a good idea for such files to contain
local variable lists to set backup-by-copying-when-mismatch
locally (see section Local Variables in Files).
The choice of renaming or copying is controlled by three variables.
Renaming is the default choice. If the variable
backup-by-copying is non-nil, copying is used. Otherwise,
if the variable backup-by-copying-when-linked is non-nil,
then copying is used for files that have multiple names, but renaming
may still used when the file being edited has only one name. If the
variable backup-by-copying-when-mismatch is non-nil, then
copying is used if renaming would cause the file's owner or group to
change.