UI stands for User Interface, something with which the user interacts with, including any physical elements (Mouse, Keyboard, etc.).
GUI stands for Graphical User Interface and is a subset of the above except that those are on screen and never physical (Buttons, Listboxes, etc.).
UX stands for User eXperience and is the thing you should care the most about in your GUIs. This is how the player interacts with your interface and how your interface affects the user.
Examples of UI Design