So you've been standing in the same place on the same corner in Chicago from Wednesday night through Thursday morning. It really hasn't stopped snowing the entire time. But what you experienced during that time was snow from two separate "storm systems". The first blast was from an "Alberta Clipper", a fast moving system that originates from the Canadian prairie provinces. They usually only last a few hours before moving on, and usually drop only a few inches of snow.
But in our case, as the Clipper moves on its way, heading off toward the Ohio Valley, the "second shoe drops." That's the Lake Effect snow that we so often encounter. Winds swirling down the lake pick up moisture off of the lake, then deposit it on the "down wind" side.
To our person who is hanging around at one location during that time, while he might not know it, he has actually experienced snow from two different "systems". In fact, the moisture for that snow has originated thousands of miles apart, the Clipper snow mainly has water that originated in the Pacific Ocean, while that lake effect snow has water that came right out of Lake Michigan.