I have observed two major terms used in academic papers/journals for citing examples : running example and motivating example. Are these interchangeable or they are to be used in a specific manner? In my thinking, I assume a motivating example’s duty stops in its section/paragraph while a running example is continuously referred to throughput the paper to explain concepts. Is this assumption correct?
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.