The data, its organization, table structure, indices, etc. combine to form the database. The DBMS is what you use to manage, view, query, and change the database.
If SQL Server is the database, Enterprise Manager is one DBMS you could use with it. With mySQL, PHPMyAdmin would be considered a DBMS. You could write your own DBMS for either of these systems...It's entirely independent from the database itself.
In some cases, database packages tightly integrate the database and the DBMS. Access is one example. In the case of Oracle, it has gone way past being a Database and a DBMS to being a CRM...A 'do it all' solution for businesses where there is a DBMS, an enormous database, and an end user interface to manage sales contacts, HR, Payroll, orders, quotes, configuration of products, etc.
-SN