_forward() just forwards everything to another controller action, while _redirect() sends a header, meaning you create a new HTTP Request and go through the entire dispatch process with it.
For instance, if you call up http://example.com/foo/bar you'd call the foo controller and bar action. If you forward inside the bar action to the baz action, e.g. within the very same request, the browser would still be on the same URL, while when doing a redirect, ZF would instruct the browser to load http://example.com/foo/baz.
Essentially, _forward() does
$request->setActionName($action)->setDispatched(false);while _redirect() does
$this->_helper->redirector->gotoUrl($url, $options);I usually do redirects when I want to prevent reload a page resulting in reposting form data.