If your "carousel" uses fade transitions, then it is not "rotating".
I don't think there is an accepted universal term. I try to stick to what it is actually doing...if it fades, it's a fader. If it slides it's a slider.
The problem is ambiguity. Overloading, as we programmers say.
Why choose an ambiguous word when a specific one exists?
Keep in mind the point of calling it anything at all is communication, and communication is a lot harder if people don’t hear what you mean.
Call it carousel, and someone either gets it, or asks what a carousel is.
Call it a slider, and half of your audience assumes you meant something else entirely.
(Also, saying a term is not “universal” is pretty much a tautology in the real world, and it is not a valid argument. And a carousel that fades between items is still rotating, just as ads are “in rotation” on the radio even though nothing turns around: yes, rotation is a somewhat ambiguous word, too.)
I don't think there is an accepted universal term. I try to stick to what it is actually doing...if it fades, it's a fader. If it slides it's a slider.