UX (User Experience) design is about how people feel and whether they find a website, a web or mobile app easy and convenient. UX designers do a lot of research and problem solving, and take care of the logic and structure of a product. In fact, they could even make paper prototypes, but graphic tools certainly facilitate the process.
UI (User Interface) design is about visuals. UI designers develop elements of the interface, such as buttons, menus, fields, and backgrounds. They select typefaces, create style (and document it in a Style Guide) if it wasn’t defined before.