Are you perhaps thinking of the term GUI? UI is not generally narrowed to refer to only visual appearance and layout. The mouse is a UI tool, as is the keyboard.
Do designers who design webpages/apps generally call themselves GUI designers?
To answer you question, no. Such people usually design interactions. Behavior. What happens when the user clicks or scrolls or drags. So they're designing UI and they're called UI designers. UX is a step removed, defining the overarching design language for the app and how it makes users feel.
In my experience there are no people who work only on the visual layout of a page and not on behavior (what you incorrectly called UI). Mockup artists maybe, but even they are usually thinking about behavior.