RDBMS is a super set of DBMS plus some more features.

Consolidated few differences here.


DBMS RDBMS
Organization, storage, management, and retrieval of data Yes Yes
Flat file design Yes No
Relational design No Yes
Password protection Yes Yes
Enforce referential integrity No Yes
Null or blank data management Yes Yes
Meta data support Yes Yes
Support relatively large set of data No Yes
Support complex business applications No Yes

Microsoft Access is an example of  DBMS.

Oracle, Microsoft SQL Server, DB2 are few examples for RDBMS.