SQL Agent running Ola scripts: all fine and perfect but a differential backup on a specific database fails
For the help of everybody I post the resolution I did found to my problem.  Scanning other forums I noticed that this I/O error 112 - "not enough space on disk" is fairly a common issue, erratic but not so infrequent.

I read a post where the issue is described to come from the sql backup algorithm which, before starting the backup operation itself, is calculating, based on DB dimension, how much space on disk will be needed. If the result (space calculated to be needed) is not enough, you get the error and the backup is aborted. Unfortunately sometime this algorithm seems to have glitches. This should be applicable on backups made with compression option on only, but in my (and other) cases may create issues independently from.

There is a TRACE OPTION which is disabling such algorithm, and the backups start anyhow without such pre-check. I've therefore set DBCC TRACEON(3042, -1) on the SQL instance, as suggested, and bingo!, now also my DIFF backups are going on smoothly.

Thanks anyhow for the interest.