Database concept - Database Management System

Database

A Database is a collection of related data that is organized so that can be easily accessed, managed and
updated. 

Database system

 A Database system is basically a computer-based record-keeping system. 

DBMS  

DBMS stands for a database management system. The database is managed by some special software packages known as a database management system (DBMS). DBMS is specially designed software to create a connection between user and program and to store data in an organized manner. The purpose of DBMS software is to allow the user to create, modify, and maintain database.

Example: MS Access, My SQL, Oracle, etc.