An application can be almost anything you decide.
In the case of your invoice example I would group all invoice related interchanges into one application. So the inbound 850 + response 997 + passing the invoice to an internal application + potentially matching against the purchasing system….
You can deploy everything into one application if you wish, i.e. invoicing, purchase orders, integrating the CRM and Financials system, etc Although you would soon regret this as management would become very difficult.
And yes you pay by processor (although a hyperthreading CPU counts as 1)