The "boxes" in the relationship graph are "table occurrences". They may or may not have the same name as the tables found on the tables tab or listed in the tables drop down on the fields tab.
You can define many table occurrences for the same table.
To learn more about Table Occurrences: Tutorial: What are Table Occurrences?
"Do all portals need to have a lineitems (or similar) table? If not when should you use one?"
A portal is simply a display method so that, when you are viewing one record in a parent table, you can also view the related (many) records to that one (if there are any). Layouts are always assigned to a specific table (see Layouts > Layout Setup and the 'show records from' pop-up). Portals also belong to a table ('show related records from' in portal setup).
Invoices is the 'one side' to LineItems 'many side' (1:n) so when viewing an Invoice, you would place a portal to LineItems on the Invoices layout so you can see all the items ordered on that invoice. :^)
If you are in LineItems layout (for example), you don't need a portal to Invoices to see invoice information because it is n:1 (many-to-one side) so you can simply place the invoice fields directly on your LineItems layout. Relationships can also be n:n.
Thanks for the quick responses.
I will follow them up.