The Design tab will show you all styles, provided you have added these in the
FormatAreaStyles.css, see the documentation for details (requires login).
You basically configure a system wide cascading style sheet for use with your format area fields. In the Schema you can then enable which classe/styles can be applied to text within a format area field. But this will also allow you to set things like the font style and size for the entire format area.
This system wide cascading style sheet is not published to your presentation system, it is only there for the format area, you basically tailor make it to what you have on your published websites. As described in the documentation, you create a
FormatAreaStyles.css in the
..\Tridion\web\WebUI\Editors\CME\Configuration\ folder of your CMS (make sure to do it for all CMS instances if you have an outscaled environment).