You can use developer tools built into your browser to see the log of AJAX requests - by checking URLs of these requests you can find what widget classes are reloaded.
For example, here is the request that reloads the address section of the checkout page:
http://demostore.x-cart.com/cart.php?target=checkout&action=&widget=%5CXLite%5 CView%5CCheckout%5CShippingAddress&_=353453461113
So, the widget that renders the first column with the address is this one:
\XLite\View\Checkout\ShippingAddress