I'm guessing the differential backups were in case of a problem with the transaction log backups, or is that flawed logic?I don't think so. What happens if the problem is with the differential backup instead of the transactional log backup?
Also differential backups are retained longer than log backups.How are you retaining the backups? Do you copy the files to different tapes?
In both cases I have selected the full backup and a differential backup from the same day.What is the device? Are you sure that you didn't have a failed full backup for the 2nd screen?
SELECT TOP 20 database_name, backup_start_date, backup_finish_date, type, backup_size
FROM backupset
WHERE database_name='DatabaseNameHere'
ORDER BY backup_start_date DESC
NOTES: Replace the database name with the correct one
database_name backup_start_date backup_finish_date type backup_size
McCoy 2016-08-23 10:00:02.000 2016-08-23 10:00:02.000 L 56517632
McCoy 2016-08-23 09:00:03.000 2016-08-23 09:00:05.000 L 256933888
McCoy 2016-08-23 09:00:03.000 2016-08-23 09:00:10.000 I 1680172032
McCoy 2016-08-23 08:00:02.000 2016-08-23 08:00:03.000 L 20602880
McCoy 2016-08-23 07:00:03.000 2016-08-23 07:00:03.000 L 24666112
McCoy 2016-08-23 06:00:02.000 2016-08-23 06:00:02.000 L 8413184
McCoy 2016-08-23 06:00:02.000 2016-08-23 06:00:05.000 I 524575744
McCoy 2016-08-23 05:00:03.000 2016-08-23 05:00:03.000 L 10836992
McCoy 2016-08-23 04:00:03.000 2016-08-23 04:00:03.000 L 5856256
McCoy 2016-08-23 03:00:02.000 2016-08-23 03:00:02.000 L 2120704
McCoy 2016-08-23 03:00:02.000 2016-08-23 03:00:03.000 I 125068288
McCoy 2016-08-23 02:41:13.000 2016-08-23 02:41:13.000 L 55666688
McCoy 2016-08-23 02:31:28.000 2016-08-23 02:31:41.000 D 25271066624
McCoy 2016-08-23 02:00:04.000 2016-08-23 02:00:04.000 L 120747008
McCoy 2016-08-23 01:00:02.000 2016-08-23 01:00:02.000 L 35741696
McCoy 2016-08-23 00:00:03.000 2016-08-23 00:00:54.000 D 25269986304
McCoy 2016-08-22 23:00:02.000 2016-08-22 23:00:03.000 L 109737984
McCoy 2016-08-22 22:00:02.000 2016-08-22 22:00:03.000 L 61171712
McCoy 2016-08-22 21:00:02.000 2016-08-22 21:00:03.000 L 59862016
McCoy 2016-08-22 21:00:02.000 2016-08-22 21:00:14.000 I 2611307520
Anyway, I don't think your backup plan is a good one. Why do you need to take a DIFF BAK every 3h?
If you're running a daily FULL BAK I even think that a single DIFF or no DIFF is even needed.
For a good backup strategy you need to know how much data can you loose. With your current strategy you can lost 1h of data. Is data ok for your client?