As a Web designer you are concerned with the visual appearance and user functionality of a website.
Your knowledge of Joomla! itself may not be advanced as you may have to deal with a wide range of content management systems while working for a range of clients. You may be contracted to supply just a template or set of templates, or you may be asked to deliver a complete working website. You are likely to be increasingly concerned with issues of accessibility and will probably want to ensure that your designs pass various standard tests.