What is the difference between DBMS and RDBMS?

DBMS :  Data Base Management System
1)A DBMS has to be persistent (it should be accessible when
the program created the data donot exist or even the
application that created the data restarted).
2) DBMS has to provide some uniform methods independent of a
specific application for accessing the information that is
stored.
3)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
4)In DBMS Normalization process will not be present

RDBMS:  Relational Data Base Management System

1)RDBMS is based on relational model, in which data is
represented in the form of relations, with enforced
relationships between the tables.
2)RDBMS defines the integrity constraint for the purpose of
holding ACID PROPERTY.
3)In RDBMS, normalization process will be present to check
the database table cosistency
4)RDBMS helps in recovery of the database in case of loss of
database due to system failure or any other reason

A DBMS has to be persistent, that is it should be accessible when theprogram created the data ceases to exist or even the application thatcreated the data restarted. A DBMS also has to provide some uniformmethods independent of a specific application for accessing theinformation that is stored.  
 Many DBA's think that RDBMS is a Client Server Database system but thats not the case with RDBMS.