RDBMS: Relational Database Management System
A relational database management system (RDBMS) is a collection of programs and capabilities that enable IT teams and others to create, update, administer and otherwise interact with a relational database. Most commercial RDBMSes use Structured Query Language (SQL) to access the database, although SQL was invented after the initial development of the relational model and is not necessary for its use.
Example: MySQL, Oracle Database, PostgreSQL etc
CRUD: Create, Read, Update & Delete
The CRUD cycle describes the elemental functions of a persistent database. CRUD stands for Create, Read, Update and Delete. (Retrieve may occasionally be substituted for Read.) These functions are also descriptive of the data life cycle.