An Oracle database consists of a collection of data managed by an Oracle database management system. Popular usage also uses the term to refer to the Oracle DBMS software, but not necessarily to a specific database under its control.
One can refer to the Oracle database management system unambiguously as Oracle DBMS or (since it manages databases which have relational characteristics) as Oracle RDBMS.
Oracle Corporation blurs the distinctions between:
Data managed by an Oracle RDBMS
An Oracle database, and
The Oracle RDBMS software itself
when it refers nowadays to the Oracle RDBMS (the software it sells for the purpose of managing databases) as the Oracle Database. The distinction between the managed data (the database) and the software which manages the data (the DBMS / RDBMS) relies, in Oracle's marketing literature, on the capitalisation of the word database.