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Difference between a database and an instance [Oracle]

The terms instance and database are closely related, but don't refer to the same thing.
The database is the set of files where application data (the reason for a database) and meta data is stored.
An instance is the software (and memory) that Oracle uses to manipulate the data in the database. In order for the instance to be able to manipulate that data, the instance must open the database. A database can be opened (or mounted) by more than one instance, however, an instance can open at most one database.