Design is a huge part of UX, acronym for User Experience. This is the very reason why a lot of designers think that a good UI or user interface makes up for a good user experience. This however, is not true. Visual design apart, the information architecture, field research, gathering and organisation and presentation of statistics, graphic arts, interaction design, usability, interface layout, gestures, the content, and the feel form an important part of the user experience or the UX
Some designers are under the impression that UX is UI. Agreed that they go hand in hand, but only for certain cases. UX and UI are not the same thing. In this awesome poster below you can see how UX is different from UI and also how people perceive UX as UI.