The letters "I" and "X" are pretty far apart on a keyboard, but type UI and type UX, and suddenly the distance between them isn't very clear at all. Both UI, which stands for User Interface, and UX, which stand for User Experience, relate to the design of a product's interface. Choose a job in one or the other and you'll be doing something very different on a day-to-day basis.
UI developers focus on the visible pieces of an application's interface. UI designers specify how specific elements are laid out on specific pages of the application. They also ensure that the overall look of the product is consistent. Their job is to make sure the application looks good using tools like HTML and CSS.
UX developers focus on the entire experience users have while working with an application. Their job is to make sure that using the application feels good, and often conduct experiments with users to identify troublesome spots in the application's flow. UX developers don't build pages; they create wireframes and storyboards to show how the application will work.
Which Career Should You Choose?
If you like the hands-on work of fine-tuning page layouts and creating graphic elements using Photoshop, working as a UI designer will satisfy your creative urges. If you tend to a more analytical kind of thinking and enjoy research, working as a UX designer will give you big questions to think about.
You don't necessarily need to choose one path over the other. At many companies, the difference between UI design and UX design isn't a hard distinction; one person may do both tasks for a project, depending on where it is in its development cycle. In those companies, whichever title your role is given, you'll enjoy the challenges of both kinds of design thinking.
You should also realize that you can choose more than once; you can change your mind. Career paths don't have to be a straight line. When you work as a UX developer, you'll work with UI developers, and vice-versa, so you'll be able to see the responsibilities of both titles. If you think you'll be happier in the other role, work with your employer to make the switch. There are plenty of design challenges to go around however you abbreviate your job title.