How do themes render caption texts in extended markup (e.g. “wp-caption” paragraphs)

That caption shortcode is built into WordPress. It should generate the same markup for any theme, unless the theme or a plugin has unregistered it and registered a replacement. I don’t know if that is the case with your theme or with TwentyEleven. Look for ‘img_caption_shortcode’ in your theme files, probably functions.php. If your theme is unregistering it, you should see remove_shortcode('img_caption_shortcode'); somewhere.

The CSS, and hence the appearance of the processed shortcode, will almost certainly vary theme to theme.