There are two main differences between a snow squall and blizzard. Duration of the event and wind.
Contrary to most peoples thoughts of what a blizzard is, it has little to nothing to do with how much new snow falls. It is about wind and it's effects with regards to lowering the visibility due to blowing snow. It is possible to have blizzard conditions with out a single flake of new snow fall. Blizzards will typically last for hours if not an entire day.
A snow squall is a brief, but very intense burst of snow that typically does not last for much longer than 20-30 minutes. Occasionally they can last for longer, especially in the case of a dominate lake effect snow band. Wind does not have to be present in a snow squall for it to happen.
The reduction in visibility in both is pretty extreme. I have been in some snow squalls that were worse than a blizzard, but been in some blizzards that were worse than a snow squall and even been in a blizzard that contained snow squalls!
-John
