SQL Server version determines backup format.
To be precise, internal DB version is what SQL Server backup and restore rely on. That version directly corresponds to SQL Server version. You can see how it's upgraded when restoring SQL 2005 to SQL 2008

>OK, then the question is, when I create a backup of a database (using SSMS), what determines the format of the backup? Is it the database engine the database currently resides or is it the version of SSMS that is being used to create the backup? And similarly, what determines the restore format, namely the database engine you are restoring to or the version of SSMS you are using to restore the database?
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>>A DB compatibility level only controls SQL Server engine behavior. What is affected is clearly stated in BOL ALTER DATABASE Compatibility Level topic for the latest SQL Version or sp_dbcmptlevel procedure description otherwise.
>>MS SQL Server supports only forward compatibility of backups for 2 versions. The backward compatibility of backups is not supported at all. IOW, SQL 2008 backups cannot be restored to SQL 2005.
>>If you want to move data in that direction, you have to use some other means.