Database management system (DBMS) is a software to manage large set of data on a computer hardware. RDBMS stands for relational database management system.
Actually they are closely related. You can say that an RDBMS is a subset/extension of a DBMS.
DBMS applications can be relational or non-relational. Note that DBMS often used in place of non-relational DBMS (one of the reason newbies get confused).
On the other hand a RDBMS application store data in tabular form with relations between the tables. MySQL, PostgresSQL are examples of RDBMS. Tables in RDBMS can have a unique identifier (called primary key). Data values are stored in the tables and each of these values can be accessible through structured query language (SQL).