A few months back someone asked about the difference between questions appropriate for mathoverflow.net and those appropriate for math.stackexchange.com. And someone answered, saying something along the lines that those appropriate for this site are at a more advanced level than those appropriate for that other site. That seems to me like a definition by non-essentials. Some questions on math.stackexchange.com are on some fairly sophisticated topics. But I think they might be inappropriate for this site simply because their answers are applications of known methods and would not be a part of anything suitable for publication, unless it's in something like a textbook.
It seems to me that what qualifies something as a "research" question may be that novel ideas are involved in answering them, that might be worth publishing for the first time in the kind of journal whose purpose is to publish novel ideas.
There are obvious reasons why such things occur more often in subjects requiring much prerequisite learning before one can even understand the question, than in things like elementary-school arithmetic. But it seems to me that defining "research" purely by the "level" in that sense is a definition by non-essentials.
(And of course, one often posts in ignorance of whether a question is a well known long-solved problem or something whose solution would be a publishable novelty. That's another complication, but not quite the point. (E.g. this one: Testing contrasts in statistics: Is this provably a hard problem, or not? I certainly didn't know if this had been done before.))
So what would be a better answer than merely the "level"?