RDBMS is extension of DBMS.

DBMS (Database Management System)

Software that provides a systematic way of creating, retrieving and managing data in a database.

DBMS Example : File System, XML, Dbase, Microsoft Access, LibreOffice Base, Fox Pro etc.

RDBMS(Relational Database Management Information System)

A DBMS based on relational model and store data in tables that related to each other.

RDBMS Example: MySQL, PostGre, SQL Server, Oracle, MariaDB, SqlLite etc.

Here area some main points that make differences between DBMS and RDBMS.

DBMS application stores data in files that have no relationship. RDBMS application stores data in tabular form which will have a relation between tables.
DBMS store data either in hierarchical form or navigational form. RDBMS table has one identifier called as primary key and data stored in tabular form.
DBMS does not support Normalization. RDBMS supports normalization.
DBMS does not provide any security with regards to data manipulation. RDBMS defines the integrity constraints for the purpose of ACID property.
DBMS does not support distributed database. RDBMS support distributed database.
DBMS is for small organization to deal with small data. It supports for single user. RDBMS is designed to handle large amount of data. It supports multiple users.
DBMS does not support client server architecture. RDBMS  support client server architecture.
DBMS have high data redundancy. RDBMS have low data redundancy.
DBMS takes more time to access data. RDBMS takes less time to access data.