The first confusion a beginner DBA encounter is what exactly Oracle is? Is it the name of Company or is it the name of product? Is it the name of database or is it the name of database management system? In order to nullify these confusions, lets start with some definitions:
A database is an informational unit. It is used to store data for future use. Database enables to store and retrieve data in an efficient and flexible way.
Database management system:
It is software by which a database is used. DBMS enables the storage, manipulation and retrieval of data from the database.
Oracle Server is the flagship product of Oracle Corporation. Oracle Server is the DBMS for Oracle Database. The word Oracle is used to describe both Oracle Server and Oracle database. It depends on the context in which the term Oracle is being used.