Well, since I started this whole thing (initially intended to be a report of interesting weather, not a debate over definitions), let me provide a little more information.
First, most of the NWS offices in the Illinois area described the precipitation as sleet in their reports and short-term forecasts, though one short-term forecast from LSX did mention a possiblity of pea-sized hail.
Second, I do not think yesterday's precipitation fit into any neat category, which is what made it interesting. I am quite sure it originated as snow, and the appearance of the precipitation under the clouds was consistent with that (i.e. it looked like convective snow showers or snow squalls look). At first, it seemed to be soft and produced the same kind of impact on the windshield as wet snow does, though it was heavier and made more noise than wet snow (though some of that was probably also the rain it was mixed with). When it was at its heaviest, there were definitely chunks of ice, as in sleet or very small hail (since the showers were convective, it could have been either), but even then I am not sure if it was discrete pellets or softer chunks that broke apart. I think what the bulk of it was was partially-melted snow that may have undergone some re-freezing - but all of it was mixed with rain.
FWIW, the showers formed and built up with temperatures around 50 at the surface but very cold aloft - but when the showers occurred, the surface temperature quickly dropped at least to the mid-40s as the cold air was pulled down by the downdrafts and precipitation. You can see this on the hourly temps from LSX yesterday; 50 at 1 p.m. then down to 45 at 2 p.m.
So as to the right definition, you decide. I think there was snow and either sleet or soft hail - more likely sleet - all of it mixed with rain. But most of it was not hard like sleet and hail both usually are, so graupel sounded like a good catch-all term to use.
Now, after all this, I do have one definitional question - would you consider snow pellets and graupel to be the same phenomenon, or different ones? I have always thought of graupel as partially melted and re-frozen snow, the stuff like yesterday that kind of breaks apart and often comes down partially melted, whereas snow pellets usually do not break, but of course are lighter and softer than sleet. I encounter them (snow pellets) a lot, both locally and while skiing out west (the convective snowshowers in the rockies can be quite nasty when they put down heavy bursts of snow pellets). They are definitely a different phenomenon from what happened yesterday, although I suppose some of yesterday's precipitation could have started out that way before encountering the warmer air near the surface. I have heard some people call snow pellets graupel, but have always thought of them as different phenomena - though I of course could be wrong - or maybe the definitions are just a little vague when applied to actual stuff that falls from the sky.
