My understanding of "Stacks" have been that they are used to raise the exhaust gases to a higher altitude, thereby allowing these gases to dissipitate easier into the atmosphere. This was an old trick used by industries to dissipitae SO2 into the atmosphere rather than in the local area. Sudbury Ontario being an eaxample. This town looked like a moonscape due to the SO2 that settled on the local real-estate. Most of the new industries today don't require as high of a stack due to SO2 scrubbers and and the pollution standards that have been imposed on them by Governments.
A stack can also be considered a buffer, an accumulator, and a regulator. Stacks typically have some variable restriction, which can be modulated to control internal pressures, mostly that of combustion chambers. Controlling these pressures translates into manipulation of combustion, and subsequently heating of the chamber. I believe chimneys are meant to carry away byproducts of combustion.
All of the above definitions are correct, a stack and chimney are essentially the same. THEY ALSO serve to create a draft effect (or stack effect) by maintaining a column of hot gas above a combustion chamber for instance. THis so-called "stack-effect" creates the needed pressure difference to carry the flue gases to the atmosohere and usually result in the desired Negative pressure inside the furnace (or boiler, etc.)
Hope that helps.
J. KAtz