The payment gateways appear in the checkout rather than opening a new page like Paypal!
It's a great option as some customers do not like to have to leave the page to pay. Personally I have found it helped with having less abandoned checkouts.
In regards to your other question about Payoneer, it is not currently available for Shopify as a payment gateway. You will need to use another gateway first and then can have the funds transferred to your Payoneer account.
Hope this helps!