Checkouts that pay with PayPal will always have to go through PayPal's checkout site. However, if you use our standard Add to Cart button codes and paste at least one copy of your View Cart code into every page that has any number of Cart buttons, not only will our shopping cart appear as an overlay within your page, checkouts for card-based direct payments will also appear within that overlay. To accept card-based direct payments, you'd need to set up any of the services listed under the Payment Gateways section here:
Also bear in mind that Buy Now buttons bypass our shopping cart to take buyers directly to instant checkout for a single item, so those will also always redirect to a freestanding checkout page whether the buyer pays with PayPal or pays you with a card directly.