Yes, the cart ID uses the session ID:
<input type="hidden" name="cartId" id="cartId" value="<?php echo session_id() ?>" />
It's best to leave the cart ID as the session ID, but you could add the ID from the orders table to the description.
on the confirm page, the description will use the FullDetails from the cart:
<input type="hidden" name="desc" id="desc" value="<?php echo $yourCart->TotalColumn("FullDetails") ?>" />
where yourCart is the name of your cart object.
you could concatenate the order ID session that is created to that:
double check the Store order Summary behavior to check the name of the session variable that will be created, for my example, the session being created is "eCart1_OrderID":
<input type="hidden" name="desc" id="desc" value="<?php echo $yourCart->TotalColumn("FullDetails") ?> ID:<?php echo((isset($_SESSION["eCart3_OrderID"]))?$_SESSION["eCart1_OrderID"]:""); ?>" />