Google Wallet actually moved to a prepaid model - you can only spend money that you add.
Android Pay works for me the way that you described Google Wallet working. I add a card number (seems like almost any card works, I have a MasterCard Amex and Visa Credit and Debit that all work) After I tap to pay Google charges my card for the amount.
EDIT: I just looked back at one of the recent tap-to-pay purchases I made with Android Pay, the charge on my card says 'GOOGNFC*[merchant-name]'. I believe that means that Android Pay charges are going through Google.