Confirmed Baskets become "orders", and in CBSubs 1.2.x also "confirmation of order" and "invoice".
Recurring payments do not generate separate invoices, unfortunately in CBSubs 1.2.x.
However you can point your user to the paypal receipt that is often also used as an invoice by many vendors.
Having invoices for each recurring payment is a feature that is scheduled for CBSubs 1.4 (CBSubs 1.3 is not far from release with a very important new feature, so we don't want to do too much changes at same time, thus it's scheduled in the very next feature release).