I am aware of Oracle. In oracle schema or user is more or less same. When we create a user, schema is created.
Database is something we create when we install oracle.
I am new to Teradata. Are things same in case of Teradata too?
How user, database and schema are related in Teradata?
The full Teradata system is quite similar to a database in Oracle.
A database in Teradata is the same as a schema in Oracle.
A user is almost the same as a database in Teradata ( you can create objects in both), the main difference is the ability to logon to the system.
And there's a hierarchy of users & databases in Teradata, root is user dbc. Users might own databases and databases might own users. A user has the implicit right to manage his children (i.e. GRANT & REVOKE access rights on owned databases & users). 
End users are usually a leaf in the hierarchy, no children & no perm space to store tables.
For more details see: About Databases and Users in Teradata
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