In order to avoid confusions between the name of the program itself (BorgBackup and Borg in short) and the backups managed by BorgBackup, the official full name should be preferred where possible, minding capitalization.
Borg or borg → BorgBackup
Borg backup(s) → BorgBackup (if it means the program) / backups with BorgBackup (if it means the backups managed by the program)
In order to avoid confusions between the name of the program itself (BorgBackup and Borg in short) and the backups managed by BorgBackup, the official full name should be preferred where possible, minding capitalization.
Based on https://www.borgbackup.org/