differences between DBMS and RDBMS

What are the differences between a DBMS and a RDBMS? Well, this is a tricky one to answer. Why? First of all, there are those that would tell you that there are not any real relational database management system (RDBMS) products available, so the answer should be given in the theoretical, instead of based on real DBMS products. I find this unsatisfactory (even though it is true). The market leading DBMS products today are all SQL DBMS products. They were originally based on the relational database management model - but did not implement the model fully or completely accurately. Anyway, let me answer it based on these SQL DBMS products versus others.
First of all, the SQL DBMS allows the data to be queried based on any column in any table. You do not need to create an index or keys in order to query data (even though indexes will help with performance and primary keys are required to uniquely identify data). So, relational/SQL data is easier to query than hierarchical, CODASYL, or some other model.
Secondly, because the relational model is based on set theory its accuracy and usefulness have a basis in mathematics. Indeed, a basis in mathematics that is centuries old and proven. This is a strong reason.
Additionally, a relational database describes data in terms of its natural structure only - that is, it excludes all details having to do with machine representation.