There is often some confusion about the difference between a view and a table in Microsoft Project. This should help clarify the difference between the two.
A view consists of a number of potential elements:
A screen (the right side typically, but may include splits. Also includes any special formatting for that screen such as modified barstyles etc.)
A table (the data displayed on the right side
A group (optional)
A filter (typically "All tasks" but may be anything you want)
Different views may access the same table or group or filter or screen but may use a different combination.
Modifying a table will affect all views which use that table.
For this reason, and because I frequently add/remove columns, it is good practice to build a specific table for each view. For example you might build a presentation view which uses a table and filter customized to show only the elements you want to present, or a print view etc.
The data displayed in the table or view does not belong to the table. It is present in the file and is only displayed in the table, so deleting columns in the table does not delete that information. Deleting a row however will delete the information.
This information is the same for all versions of Project, with the exception of Project 98 and earlier which did not have grouping.