UI: User Interface - the layout & visual look & feel of the page/components.
UX: User Experience - the interactions of these pages/components by the user (incl. expected behaviour etc.)
> you seem to be using a particularly narrow definition of "designer" here
My definition of UI designer is somebody who designs UI (which encompasses those of print background which a lot will probably have been at some stage in the/their past)
> but it's mostly orthogonal to their role as programmers
No, it's not, unless your programmers have been relegated to code monkeys. In years gone past (pre web dominance, when native desktop applications ruled), developers were designers/user experience etc.. which lead to the checkboxes everywhere UI.
Good UI needs someone with good design aesthetic. This is where UI designers shine.
In contrast to other design fields(most notably Industrial Design, where designers have pretty much always owned (& thought about) design & interaction as a whole), that is not something which UI designers have done. It's only in recent years that I've seen UI teams claim UX in the form of renaming themselves as "UI/UX team".
My point is that UX has not historically been something they've put much thought into ,and as a result, they are not qualified to just own UX.