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It is not uncommon in the IT industry for different vendors to use the same word to mean very different things. Database is one of those words.
The word database is often used by PeopleSoft to refer to the collection of tables in the PeopleSoft administrative schema within an Oracle (or other) database. In contrast, Oracle would describe a database as the collection of physical data, log files, and control files. An Oracle instance is the collection of intercommunicating processes that administer the database. The importance of these distinctions will become apparent as I describe the signon process.
Sometimes even DBAs are guilty of using terminology carelessly. Unless you are running Real Application Clusters (RAC), there is a one-to-one relationship between instances and databases. You may hear DBAs talking about starting the database when really they mean starting the instance.