Technically speaking, a database is really the collection of related data and the relation-
ships supporting the data. The database software—a.k.a the database management
system (DBMS)—is the software, such as Oracle, Sybase, MySQL, and DB2, that is
used to store that data. A database engine, in turn, is a process instance of the software
accessing your database. Finally, the database server is the computer on which the
database engine is running.
In the industry, this distinction is often understood from context.