It's interesting that job ads always say UI/UX, putting the UI first. That's the part that non product designers see, and that's what they, consciously or not, think is the most important part of a product or website.
As a UX designer, I think about a lot of things that the UI designers I work with don't: what's the error state? What's the empty state? How does the UI need to change for mobile (beyond just shrinking everything down and stacking it, LOL).
What are the UX best practices around use of accordions? Around mega-menus for navigation? How does our particular user base differ from the ones cited in best practices articles, and what does that mean for how a feature gets tested and built? What kind of success metrics do we have for a feature? How can we use analytics to answer usability questions after launch? How do we craft good questions for a user testing session? And on and on.
The best UI designers not only can make esthetically appealing interfaces, they also understand Gestalt principles AND know how to design for accessibility. Those skills are separate from what UX designers bring to the table.
Unfortunately, since both jobs have "design" in their title, many people think they can just be lumped together and done to high standards by one person. Which ends up giving short shrift to either the UX part or the UI part.
Interestingly enough, most employers do get that "developer" in a job title doesn't mean you'd hire one person to do both front-end and back-end development, or both develop for Android and iOS. But when it comes to the word "designer" it's like blinders go on.