A database is a container with an allotment of space in which users can create and maintain database objects, including tables, views, triggers, indexes, stored procedures, user-defined functions, and macros.
A user is similar to a database, except that a user has a password and can log on to the system, whereas a database cannot.
The primary Teradata Database user is DBC, which owns all system disk space and contains the Data Dictionary tables and other system objects and information.