You've hit one of the core problems with this emerging career field. I would say most people don't know or fully understand what UX is. Many employers have heard UX as a buzzword, and are just beginning to recognize UX as an important aspect of the design and development process. As a result, UX is often confused with UI, and many people taking on UX roles end up doing more UI work than anything else.
The basic answer I go with is "User Interface is the controls you use when working with a website/piece of software/etc. User Experience is how you feel about using those controls."
I took this idea and ran with it in my blog post for today, which goes into more depth if you're interested.