What is database or database management system(DBMS)?

A database is an organized collection of data, generally stored and accessed electronically from
a computer system.

A database management system(DBMS) is a software package designed to define,manipulate,
retrieve and manage data in a database.

A DBMS generally manipulates the data itself, the data format,field names,record structure and file structure.

Examples of DBMS are:

mysql
access data
sql server
oracle
mongodb
postgres

What is the Difference between DBMS and RDBMS?