“If you stay on the right track for too long, you could get run over.” ~ Will Rogers, American Satirist
Here are some working thoughts on the difference between UX and UI:

UX/ UI is Two-Faceted: It Cleans and Plants Seeds:

UX Designers originally were ergonomists for the digital arena. Our intent was to make the interface as accessible, and easy to use, as possible. We succeeded. Nowadays, UX designers are “interior designers” for websites. They follow contemporary trends (such as “responsive websites”), using accessibility guidelines that have now become commonplace (as have most SEO practices).
User Interface architects interpret UX findings, (which can also include usability studies, research, competitive positioning, etc.) to build conceptual models that can be used throughout most stages of development – from specification writing to use case analyses to QA testing.
User Interface Architects are Structural Engineers for websites. We assess the relationship of objects and provide ideal taxonomy for categories and navigation, in addition to ideal journey to destination flows.
Both are Digital Strategists, and they work in concert.
UX4UI Experts audit processes, systems and design, and then provide a report that summarizes findings and provides recommendations on how to best move forward. UI4UI experts are equally logical and creative. We can’t help but improve all that we see. Our minds naturally ideate.