rdbms is a relation data base managment system and dbms is a data base managment system. rdbms is two table joning the relation and dbms is not join the table.
The major differences between DBMS and RDBMS are: DBMS is mainly a storage area and it does not employ any tables for storing the data or does not use any special function keys or foreign keys for the retreival of the data. RDBMS has the major difference of solving the queries easily as they are stored in table format and use many functional keys in solving the queries. They follow the Codd's rule..