How can an existing user login to check on previous orders?
The Drupal site login and Commerce login are definitely the same; check the login details again.

Commerce 2 supports checking the details of orders out of the box.

It adds an "Orders" tab to the user profile (/user/UID/orders), and a view (that you can customize if you like) is provided to display the order history (/admin/structure/views/view/commerce_user_orders/edit/order_page).