I'm not a native English speaker and I've read the descriptions in BOL but still can't understand what exactly are they. Can anyone explain in an easy understand way?
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The screenshots from SSMS will help you understand the terms:
backup set - is a backup from a single, successful backup operation. E.g. a full database backup created at 8 AM yesterday
You can see that there are 2 backup sets in a single backup media set
backup device - a disk file or tape drive
backup media - tapes or disks where backup are stored backup media set - in the screenshot - it's the BAK file where backups are added
backup media family - You're creating the 8 AM full database backup and your database is huge, the backup takes more space than 4 tapes can store. Say you have 4 tape devices that are used to backup your database. When one tape is full, you insert a new one. If your database backup takes 20 tapes, that's 5 tapes per each tape device. The 5 tapes created on the tape device 1 belong to the same backup media family, as they have the same "father" - tape device 1