Hi,
I guess the diagram is more about Ariba Buyer than Ariba Network and Ariba Discovery,
The Diagram shows the various types of setup you can have in Ariba Buyer (On - Demand)
1. Complete Procure to Pay module
2. Procure to Order in Ariba and send the Order to back end ERP system to continue the Invoicing and Payment There
3. Use Ariba just for Procurement Content ( i.e only for catalogs) send the item to ERP and create Requisition,Order,Invoicing and Payment there.
4. Buy and Pay Service item in Ariba
5. create Procure to Order in ERP and use only Invoicing and Payment
On your second question, yes Ariba allows you to do Procure to Pay if you go with the 1st option i listed above, however, in real time scenario's Ariba is mostly integrated with an ERP system, because customers usually manage Accounting, Budgetings, Taxation, Asset Management, Inventory Management in the ERP system and consider that as the source of truth, thereby sending updates depending on individual cusomter requirement back to the ERP.
Good to know that you are writing thesis on Ariba, will be able to share it with me, ofcourse this will be for reference purposes and I wouldn't use it anywhere, my ID is pranezmehta@gmail.com