Database:   

A collection of data organized in a manner
that allows access, retrieval, and use of that data.

Database Management System (DBMS):   

A software tool that allows you to use a computer to
create a database;
add, change, and delete data in the database;
sort the data in database;
retrieve data in the database;
and create forms and reports using the data in the database. 

One example of DBMS is Access.