As someone who changed their title to UX designer (And gave up CAD for the 2D kind of wireframe) there are a lot of naming confusions involved.
Ultimately you can call yourself whatever you want, UX tends to be the broadest, higher level version of the term. There is a great lack of consistency across the industry since it's still a young-ish and constantly evolving field.
You have Interaction Designers (typically focused on specific digital interactions and user interface design), Visual designers (who may be doing interaction, may be doing UX, but have the specific skillsets in making pixels look great), User Experience designers (who may do both of the above, but will also have a higher view of looking at every part of the customer journey, from digital aspects but also including things like physical hardware interaction, packaging, etc).
If you look at job descriptions the two are often used interchangeably, because it's hard to point to certain examples and say "this is UI" and "This is UX".
My favorite example is the cereal metaphor that was passed around years ago. http://edlea.com/blog/product-ux-ui-cereal/
The User Interface is ultimately the way a customer accesses your product. User Experience is someone who considers every part of the customer experience including the information architecture, product features, to what makes them buy it in the first place. A bowl of cereal can have a delicious cereal and fancy spoon, but if the milk is sour the whole thing tastes like sh*t. That is the importance of UX over UI.