Tables and Layouts are separate.
You can have several layouts that view data from 1 table.
Adding fields to the table, doesn't necessarily add it to any layout. You can set individual layouts to automatically add new fields, but you need to be viewing the layout when you add the field in Manage Database screen.
You can insert a field manually on a layout...and even select the table occurrence that it shows data from.
As for "Table" view, "Form" view and "List" view...you can have a layout display whichever one you want. Typically, if you are going to go between the 3 views (or give the option), you would create 3 separate layouts, that way you can control the way each one looks. Although that is not absolutely necessary.
Thanks - good to know - thought I was going to lose my mind.