RDBMS is a sub category of DBMS. A DBMS could be of heirarchical object orianted etc. RDMBS is a kind of DBMS which deals with records in diffrent tables have some relation between them.
A DBMS has to be persistent that is it should be accessible when the program created the data ceases to exist or even the application that created the data restarted. A DBMS also has to provide some uniform methods independent of a specific application for accessing the information that is stored.
RDBMS is a Relational Data Base Management System Relational DBMS. This adds the additional condition that the system supports a tabular structure for the data with enforced relationships between the tables. This excludes the databases that don't support a tabular structure or don't enforce relationships between tables.
