Formally speaking, the difference between a user and a database is that a user has a password and a database does not. Users can also have default attributes such as time zone, date form, character set, role, and profile, while databases cannot.
You might infer from this that databases are passive objects, while users are active objects. That is only true in the sense that databases cannot execute SQL statements. However, a query, macro, or stored procedure can execute using the privileges of the database.