DBMS is software that manages and provides access to data stored in a database. RDBMS is an advanced version of DBMS that stores data in tables for more efficient access. The key differences are that RDBMS stores data in tables rather than files, supports distributed databases, stores larger amounts of data with less redundancy using keys and indexes, and supports multiple users simultaneously whereas DBMS only supports a single user. RDBMS also has higher software and hardware requirements.