Yes a blizzard is worse than a regular winter storm.
Actually a blizzard and a winter storm with snow are the same thing at least partially because both a blizzard and a winter storm are defined as an intense snow storm with strong winds blowing the snow around with reduced visibility.
However with a blizzard and a winter storm the blizzard has a much stronger wind gusts blowing the snow around in the air instead of just a winter storm that the wind is blowing not as fast or strong.
Both winter storms and blizzards are dangerous winter weather events and you really should stay home and off the roads during those blizzards and winter storms for your safety.