If the person providing the supplementary stimulation can identify the upcoming response, the type of supplementary stimulus is called a prompt. If they cannot, then it is called a probe. It does not matter whether the supplementary stimulation is formal or thematic, nor does it matter who provides the supplementary stimulus.
A discriminative stimulus with the following features:
It is a supplementary stimulus
The person providing the supplementary stimulus can identify the response that the speaker is likely to emit
It is a supplementary stimulus
The person providing the supplementary stimulus cannot identify the response that the speaker is likely to emit
Whether the controlling relationship is formal or thematic
Who provides the supplementary stimulus (either another person or the speaker him or herself)