What's the difference between Engine company and Ladder company?

The engine crew stretches the hose and puts out the fire. The ladder crew(truck in Chicago) searches for victims and does ventilation of the building. Then there is the Squad that assists with all of those on a working fire, not shown in the movie for some reason.

Also, an Engine Company operates a Pumper Truck, which has a pump and carries water and hose to a fire, while a Ladder or Truck Company operates a Ladder Truck, which is fitted with an Aerial Ladder or a Tower Ladder/Snorkel(bucket/boom) device and carries search/rescue and ventilation equipment, as well as additional ladders to a fire scene. An Engine is responsible for putting the fire out, while a Ladder or Truck is responsible for search/rescue and ventilation/forcible entry.