A Database is an organized collection of data, generally stored and accessed electronically from a computer system.
A database management system (DBMS) is the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS software additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a "database system".
Often the term "database" is also used to loosely refer to any of the DBMS, the database system or an application associated with the database.