When you configure the checkout wizard you will need to select your Payments Gateway then you will need to add in the needed details for your gateway. In the last page of the checkout wizard is a screen that shows all of the pages that will be used and the names of them. Here you can alter any of the page names that it uses by default with your own page names.
When you finish the wizard it will create the complete checkout experience. If you use a local checkout you will stay on the site the whole time and get to either a checkout success page or a failure page.
What gateway are you using and how do you have things setup currently?