In Magento, the approach is somewhat different.
Basically, Magento uses Blocks which are associated with templates in the view, so each page consists of both a block PHP class (they all inherit from Mage_Core_Block_Abstract) and mostly (but there are exceptions) an associated template (phtml file).
To render partials, blocks can have child blocks within them with given child names. From the parent block, you can render the child blocks using getChildHtml($childName).
To set variables at the child block, you can use the magic getter and setters, because all block PHP classes ultimately extend from Varien_Object.