In CakePHP, $this->redirect() and $this->render() are two different methods used in controllers to handle the response and flow of the application. 

$this->redirect() is used to redirect the user to a different URL or action within the application. It is commonly used after processing a form submission or when a specific action needs to be performed, such as redirecting the user to a different page after a successful login. The redirect() method sends a HTTP 302 status code to the browser, indicating a temporary redirect, and triggers a new request to the specified URL or action. 

On the other hand, $this->render() is used to render and display a specific view template in the current request cycle. It is often used to explicitly render a view different from the one corresponding to the current action. For example, if you want to render a specific view template instead of the default template associated with the current action, you can use $this->render(‘custom_template’).