Full and differential restore with two backup files - SQL Server 2008
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.

More information about backup devices can be found here: http://msdn.microsoft.com/en-us/library/ms179313.aspx

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.