What will be inside the last differential backup file?
I'd definitely recommend that you read A SQL Server DBA myth a day: (30/30) backup myths from SQL Server expert Paul Randal for some really good information about SQL Server backups.  

To answer your immediate question, the lastest differential backup (diff_backup_2018_05_09_008000.bak) in your question would contain all changed pages since the last full (non COPY_ONLY) backup (full_backup_2018_05_09_000000.bak) **PLUS ** enough of the transaction log to be able to recover the database to a transactionally-consistent view of the database at the time the data-reading portion of the backup finished.  Transaction log backups would not affect what pages are included in full or differential backups