Difference between running example and motivating example
A motivating example provides motivation for a definition, a theorem, or even the whole paper. A running example is an example that is recalled time and again during the paper, applying the newly discovered knowledge to it, presumably to show how things work. It is possible for a motivating example to also be a running example – there is nothing that prevents you from reusing the same motivating example several times in the paper.

I still have enough faith in academia to say that no reviewer will be petty enough to tell you that the example you called "motivating" should have been called "running" instead, in any case.