Full form of DBMS: Database management system
Full form of RDBMS: Relational database management system
Basically, RDBMS is the extension of DBMS.
In DBMS data is stored in a file or we can say that a hierarchical form or a navigational form, whereas in RDBMS data is stored in Tabular form.
The DBMS does not support distributed database, Normalization etc. whereas RDBMS support.
In RDBMS there is a concept of primary key, foreign key etc. but there is no such constraint in DBMS.
Example of DBMS is XML or any file system.
Example of RDBMS is Postgre, SQL Server, oracle etc.