They can be shut by system activation, or zone activation. Zone activation is what you're describing - the system in the rest of the building stays in "normal" mode, but if there's a detector off on the 2nd floor, then the 2nd floor HVAC gets isolated.
General activation (not sure if that's the "proper" term) shuts down the HVAC in case the fire alarm goes off, and doesn't turn back on until the system resets, or FD activates it (see below).
We've also seen them tied into duct detectors - smoke in the duct shuts down the system, and the dampers. When the FD resets, system goes back to normal. Usually the duct dectector is wired to an LED on the outside of the duct, or in the adjoining passageway, to assist in locating the detector.
Fancier systems also have an "FD" override, for evacuation of nuisance smoke - basically, it's a preset where the fans will turn on, and certain dampers will open to exhaust fumes / smopke from an area, but only if the FD / building security activates that aspect of the system.