One is measuring duration, while the other is a measure of intensity. Snow showers means that you'll get short bouts of snow -- i.e., it can be snowing for an hour, then stop for two. It also means it might be snowing in some places around the area, but not others. (Same idea goes for "rain" showers or "thunder" showers as well.)
On the other hand, flurries is the rain equivalent of drizzle -- just a couple of flakes here and a few flakes there that don't amount to anything on the ground.