Website Designer, Web User Interface Designer, Web Developer, Graphic designer, User Experience Developer all these terms have specific definition but come to final work almost same. In level 1-3 companies you need to learn everything, do every task. When work in level 4-5 companies, then we will get special roles and single product development or projects with a single team.
So basically my suggestion for you learn everything related to U I and graphic design like Photoshop, html, css, jQuery, then we can move ahead with advanced level of programming also.