The question's a bit vague. RDBMS=Relational Database Management System which comprises a number of tables that contain related information and a whole stack of software (the Management System) that manages the data. Probably what you need is a book on Databases.
#1 A DBMS has to be persistent, that is it should be
accessible when the program created the data ceases to
exist or even the application that created the data
restarted. A DBMS also has to provide some uniform methods
independent of a specific application for accessing the
information that is stored.
RDBMS is a Relational Data Base Management System
Relational DBMS. This adds the additional condition that
the system supports a tabular structure for the data, with
enforced relationships between the tables. This excludes
the databases that don't support a tabular structure or
don't enforce relationships between tables.
#2 DBMS does not impose any constraints or security with
regard to data manipulation it is user or the programmer
responsibility to ensure the ACID PROPERTY of the database
whereas the rdbms is more with this regard bcz rdbms difine
the integrity constraint for the purpose of holding ACID
#3 DBMS are for smaller organizations with small amount of
data, where security of the data is not of major concern
and RDBMS are designed to take care of large amounts of
data and also the security of this data.