Definition of snow, snow flurries and snow showers;
Snow: This refers to the white, cold, flakey stuff itself. It does not describe any particular manifestation thereof.
Snow Flurry: Light, intermittent snowfall without any significant accumulation of snow on the ground.
Snow Shower: A short duration of light to moderate snowfall. Snow showers are characterized by their sudden beginnings and endings -- they're finite. They usually leave snow on the ground, but not always. Also, snow showers come from cumuliform clouds, as opposed to stratiform clouds.