Yes, the firebox is generally off to one side, or in the case of a few smokers, in the back, but it isn't directly in line with the cook chamber.
Vertical smokers have the heat source directly under the cook chamber, and it will be in the same structure (think Weber Smoky Mountain or Drum smoker).
There are gravity fed smokers, pellet grills, and probably a few more that slips my mind, but no doubt you will see all of them here.
Chett, PM me if you have any questions. I don't want to highjack this thread.