Errors restoring a differential backup
Here's what I have understood from your question : 

Your Full backup taken yesterday failed to restore on your TestingDB. Hence, you took a latest full backup and that got restored successfully. After this you are trying to restore a differential backup from yesterday. 

This will not work. Here's the reason it will not work. Everytime a backup happens let it be FULL\DIFF or LOG. it generates an LSN, this LSN is a chain and unique number which matches with each other and are compared at the time of restore.

If you have taken latest FULL backup then now you should take the latest diff backup and try to restore it on TestingDB and you should not get any errors you received earlier. Also, while restoring you can check the LSN of Full and Diff backup files by using RESTOREHEADERONLY  command which reads the headers of your .bak file and gives you the information about First and Previous LSN.

I hope this helps in solve your problem.