Web Design = Making pretty websites... These are typically the art oriented, graphics design guys who create the mock-ups and beautiful layouts and will be required to translate those onto the web via HTML/CSS. These guys have to know browsers in depth and know concepts such as responsive web design. Some of these guys may dabble a bit in Javascript, but nothing too serious. Web designers know layouts, visual design, typography, etc in detail.
Web Development = more of the programmers of the web world. If you want your world to be more than a pretty page, this is where you will end up. There are typically two sides to the web-world. There is client-side and server-side. Client-side is dealing with the browser side of the equation and you will be using HTML/CSS and Javascript to create behavior for your pages. Server-side is where languages like Ruby with the on Rails framework, PHP, Python with the Django framework, Javascript with Node.js, etc., come into play. You will typically have to know some sort of database as well. Back-end development deals with serving up data that clients request from the server and things of that nature. "Full stack" development means you do both client-side and server-side development.