Web design is the client-side view of a web page. Typically, it is the process of developing a web site or a web site structure and often contains visual elements on a web page, and this is done by using graphics programs such as Adobe Photoshop, Macromedia Fireworks, Corel Draw, etc. and provides a framework for the look of a Web page. It includes the layout, navigation and site colors. And who designs a web page is called web designer in web design company's terms.
Web development is back-end of the web site. It is the programming in the back end which converts the beautiful design into a good working and professional website meaning websites needs a login , offer useful tools for the users, provides some flexibility to customers such as a shopping cart or online payments so this all coding or programming done in web development. And Who doing this programming called web developer.
Web design is the only graphical representation of a Web site does not contain code where web development is all about coding to handle all requests from the web site and is commonly used to describe programs that required to construct the "back side" of the website.