I am probably more of a "layman" than most of the regular posters on here and, yes, I consider Eglinton to be, mostly a subway. As for those above, i bet you the average guy's nomenclature would depend on how much of it goes underground. To use Calgary, very little of it goes underground and where it does it is to get around/past something so most probably don't think of it as a subway but as an LRT with some bits underground. Kinda like the Spadina line here or if, say, the Hurontario line went underground from Steeles to Brampton GO (as some would want) it would still be an LRT with a bit underground.
That may "offend' some definitions (it is not meant to) and if it does I think people offended by that may have to get prepped for the years after 2020 when a lot of people talk of getting on the little subway on Eglinton (just my guess at how it will be tagged).