Email provider-  is so a store owner can collect the information but not process credit cards or shipping.  The email provider sends the store owner a notification of interest or a pending order (anyone please feel free to correct me about this).  I am sorry I dont have this module installed anymore or I would check it for you.  I do know that Catalook has a speacial setup for what you are looking for.  

On another note, I do think the store owner does get a nofification of an order email on either of the above modules.

To answer your question concisely, the Email Provider uses the Host's SMTPServer setting.

The technical details for anyone who is interested: In actuality, all the email payment provider does is finalize the order calling the store checkout control's GetFinalizedOrderInfo method. This method totals the order, ensures there is an order (if there isn't one it would get created here), and then immediately calls the PaymentControlBase generateOrderConfirmation method (the method which generates the nicely formatted email notification called by ALL store payment providers. This method sends a copy with the subject StoreInfo.Name + "Order Confirmation" to the customer's email address, and sends a separate copy with the subject "New Order: " + OrderID to the email address specified in the StoreInfo.DefaultEmailAddress setting configured on the admin page.

More Info on WWStore for anyone who is interested: The WWStore module is a subtly enhanced version of the original core module released in Jan 2006. It is essentially identical to the original save that it is a complete solution. The WWstore module includes the Email provider as noted in this thread, as well as a rudimentary order management capability, lacking in the core store module.

My portal root is C:\Inetpub\DotNetNuke4. When it was C:\Inetpub\Sites\DotNetNuke4, I had problems. Hope this helps.