We recently moved our website to a new dedicated server that has SQL Server 2005: Studio Express.
SQL Server 2005 Express is a version of SQL Server. Microsoft SQL Server Management Studio Express is a client utility used to manage SQL Server 2005 (not sure if it can only manage SQL Server Express or the other versions of SQL Server 2005 as well).
SQL Server Express has numerous limitations, most notably in DB size and memory usage. What is the size of your database? What were you using before for your database?