You will need to set up a separate backup device for the FULL and the DIFF. When you create the Backup Device it is a single file. You can't save a FULL and a DIFF in the same Backup Device.
If you are trying to restore the database over an existing database and want to replace the data you will need to use the WITH REPLACE option in the restore. More information can be found here: http://msdn.microsoft.com/en-us/library/ms186858.aspx
REPLACE should be used rarely and only after careful consideration.
Restore normally prevents accidentally overwriting a database with a
different database. If the database specified in a RESTORE statement
already exists on the current server and the specified database family
GUID differs from the database family GUID recorded in the backup set,
the database is not restored. This is an important safeguard.
The REPLACE option overrides several important safety checks that
restore normally performs. The overridden checks are as follows:
Restoring over an existing database with a backup taken of another
database.
With the REPLACE option, restore allows you to overwrite an existing
database with whatever database is in the backup set, even if the
specified database name differs from the database name recorded in the
backup set. This can result in accidentally overwriting a database by
a different database.
Restoring over a database using the full or bulk-logged recovery model
where a tail-log backup has not been taken and the STOPAT option is
not used.
With the REPLACE option, you can lose committed work, because the log
written most recently has not been backed up.
Overwriting existing files.
For example, a mistake could allow overwriting files of the wrong
type, such as .xls files, or that are being used by another database
that is not online. Arbitrary data loss is possible if existing files
are overwritten, although the restored database is complete.
Best Answer
I believe @Les H has already answered and Yes, ola's script should do the work here without any issues.
However as per the MS Link you can also do something like:
Use SQL Server Management Studio Express or Sqlcmd to create the following stored procedure in your master database named
sp_BackupDatabases. The script to create the SP is available on the link.create a batch file that will execute the above SP, also specifying the location of backup and its mode, that is Full , differential or log.
Schedule a job by using Windows Task Scheduler to execute the batch file that you created in step 2