In Oracle, the instance is the collection of memory structures and processes running on the server.
The database persists when the server is shut down. The instance terminates when the server is shut down. The instance provides the gateway to the database. You cannot access the database while the instance is down.
Normally, there is a one-to-one relationship between the instance and the database. If you have Real Application Clusters (RAC), then you can start multiple instances accessing a single database. This lets you start Oracle on multiple servers, but all accessing the same data.
It does not make much sense to have one Oracle 11g RAC instance access multiple databases. How is Oracle to know which database a modified table belongs to?
Other database systems like mySQL and SQL Server have a concept of multiple databases. In those systems, their term of "database" does not match Oracle's term. The closest Oracle has to a SQL Server database is the "schema". In Oracle it is definitely possible to create multiple schemas in the same database, all accessible in the same instance. And you do not need RAC to do that.
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