Magento 1.8 – Replace Block in Layout for Specific Page

Erfan is right that the html is outputted twice, once as a child of 'checkout.onepage.login' and once as a child of 'checkout.onepage.billing'

Thus there are two child blocks with the same name. Each can have a different template, and each gets rendered as a child of the parent.

To change the persistent block in either of the parent blocks, you need to target the parent block directly such as:

<checkout_onepage_index>
    <reference name="checkout.onepage.login">
            <block type="persistent/form_remember" name="persistent.remember.me" template="my/custom/template.phtml" />
        </reference>
</checkout_onepage_index>

The above will only change the template in the login block.

If you only target the child block 'persistent.remember.me' then magento seems to only change the occurrence of the first found block. Start Speculation: This is most likely in order or alpha occurrence , with 'checkout.onepage.billing' appearing alphabetically before 'checkout.onepage.login', in whatever array is used to store the block internally. The fact that .billing is rendered after .login just makes it look like it is only changing the second occurrence. :) End Speculation

Each order idem has a product associated to it, because that's what you buy...products.
And each product can have a different type: simple, configurable, grouped, bundle, downloadable, virtual.
Each product type may behave differently in certain conditions. For example the price should be shown differently depending on the product type.
The method addItemRenderer provides a block and a template for different product types.
To show a line in an order for a product the method Mage_Adminhtml_Block_Sales_Items_Abstract::getItemHtml is called.
This method checks the product type and looks in the associated renderers for a block and template to use.

public function getItemHtml(Varien_Object $item)
{
    if ($item->getOrderItem()) {
        $type = $item->getOrderItem()->getProductType();
    } else {
        $type = $item->getProductType();
    }

    return $this->getItemRenderer($type)
        ->setItem($item)
        ->setCanEditQty($this->canEditQty())
        ->toHtml();
}

This method calls getItemRenderer that looks if there is a block and a template associated to the product type. If there is it uses them. If not it uses the block and template marked as default.

The method is somehow similar to adding a child block to a parent block, but it's some kind of conditional child block. You have have multiple renderers associated to the parent block, but only one is used depending on what you are printing. And the renderer can be used multiple times. Each time a product of the same tipe is shown, the associated renderer is used.