prompting and cueing/cuing can mean almost same thing. However, it's complicated.
A cue is when a person signals to you to do something. The cue for you to begin singing is when the music director raises both hands together. Cues are signs given by people to make other people do things or instruct them to do things or to start to do things. They are also something you interpret as a sign to do something. We say: verbal cues. But cues can be physical or even musical.
In the theater, if an actor is not on the stage, he listen for some dialogue or music or some action on stage and when he hears or sees that, that it is cue to go on stage and do his thing.
A singer might go on stage when another singers leaves. When the other singer leaves, that it is his cue to go onstage himself. Cues can be interpreted by a performer (actor or other) or they can be given to him, by a stage manager giving him a hand signal.
A prompt is more specific: in the theater (again), prompting means when an actor forgets his lines, a prompter (sitting in a little box at the front of the stage, traditionally or in the wings) whispers his lines so the actor can remember them. They usually whisper the next lines.
So, something can be a cue for someone (the person knows this in advance) or a person can be given a cue by a stage manager. Prompting is really just reading out some part of a text, so a person remembers their lines.
I would avoid saying classmates give other classmates cues/prompts so they do not get a bad mark. In any case, a teacher would see that. It almost sounds like cheating.
However, a teacher or pupils can be doing exercises that involve cues or prompts from the teacher or from each other. That yes.