DBMS and RDBMS both were coined for the database systems. Although, they are used for storing information in the physical database, yet they have various differences between them.
We will talk about the difference in a clear way for easy understanding. DBMS (Database Management System) and RDBMS (Relational Database Management System) have a large use in computers.
DBMS (Database Management System):
DBMS stores all the data in a file format. These are basically stored in navigational or hierarchical form. These are not as secured as RDBMS, in terms of manipulation of Data.
Normalization is not used in DBMS. Hence, if this constraint is not required in the project, then one can go with DBMS. It also uses a file system to store the data. This destroys the relation between tables.
Not only this, one has to provide a proper uniform method to access the stored information. The distributed database feature lacks in DBMS. And is generally meant for small organizations with a single user or less data.
RDBMS (Relational Database Management System)
Security is tight in RDBMS, as it strictly follows ACID property (Atomicity, Consistency, Isolation, and Durability). It also follows Normalization. All the data are stored in a tabular format.
Each table can have a unique primary key and data present with attributes in the column. RDBMS supports tabular data structure, and thus maintains a relationship between stored values. It also supports the Distributed Database feature.
RDBMS is generally used in big corporates, where a large amount of data is handled and multiple and complex relationships are required.
Hence, in conclusion, one can say, RDBMS is an extension of DBMS. There are many software products that use both, but all of these depend upon the usage and requirement. Examples of DBMS are file system, XML, JSON, etc. Examples of RDBMS is, SQL, Postgres, MySQL, SQL Server, Oracle, etc.