RDBMS is a super set of DBMS plus some more features.
Consolidated few differences here.
|Organization, storage, management, and retrieval of data||Yes||Yes|
|Flat file design||Yes||No|
|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.