Summary:
A Project User Defined Field is different from a Task User Defined Field.

The Project User Defined Field is displayed only on the main page of the project. The custom data in this field applies to the entire project, and is not available for each Task or Sub-task of the project (refer the attached picture).
This allows entry of custom data specific to the project, and need not be entered for tasks and sub-tasks.

The Task User Defined Field is displayed for all the tasks and sub-tasks in the project including the top level (Project level) (refer the attached picture)