Web Designer — Probably went to school for graphic design. This role has mostly been replaced by UI design since the rise of appreciation for good user experience.
UX Designer — Often a researcher that brings the site to the stage of wireframes and prototypes.
UI Designer — Designs the look and feel of the site, often creating an advanced prototype.
Although it starts off mostly talking about Computer Science students, the discussion of design and interactivity careers is very good. It’s an important read for soon-to-be graduates interested in web careers.
Soon you will be meeting teams of people. All of them with very different responsibilities and skills. This article helps differentiate the forest from the trees.