RDBMS 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.
Yes you can say 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 because RDBMS define the integrity constraint for the purpose of holding ACID PROPERTY.
Eg of RDBMS are : Oracle , SQL SERVER
Eg of DBMS is : File.