A flue is not always the same as a chimney.
A chimney is a brick or metal structure that contains one or more flues. It is what you see running up the sides of houses and / or sticking out of roofs. It is best thought of as a support structure that contains the flues.
The flue is actually the pipe or passage that the smoke from an appliance travels through.
Typically each fuel burning appliance, such as a furnace, stove, fireplace, etc. will need to have its own separate flue, so many times they will put several flues into the same chimney structure, especially when dealing with masonry chimneys.