I'd classify stuff on a sliding scale. If the particles have such low rest mass that they're moving close to the speed of light, they count mostly as radiation, not matter. If the particles are much heavier than the temperature and so are moving slowly, they count more as matter, less as radiation.

I don't think you want a classification scheme to have discontinuities. Rest mass zero, radiation; rest mass an epsilon higher, not radiation isn't kosher, since one can never confirm a physical value is precisely zero.

All an argument for Fuzzy Logic, I guess.