I have a different view about this concept. DBMS is basically set of system programs which helps to store, retrieve and manipulate the database. If this system programs support a database (to perform the above mentioned tasks) which got designed using relational theory (or methodology), then it is called as RDBMS.
Same thing is applicable to Hierarchical and Network models.
In short, DBMS is an abstract concept and RDBMS, NDBMS, HDBMS are specific implementations depending upon the data model used.