Without any other info, I would say that notification and indicating circuits would fall in the same category; these would include horns, strobes, and horn/strobes. "Indicating" may refer to lights, printouts, or other indications at a constantly manned station, i.e. not for public alert, but without NFPA 72 in my hands that is a statement based on semantics.
Initiating devices can be either alarms or troubles. Some alarming devices would be smoke detectors, heat detectors, manual pull stations, fire water flow meters, etc. Most often alarming devices will initiate a public address system and engage any life safety devices associated with the alarm, e.g. releasing door locks on egress routes. Trouble devices typically monitor FA wiring for an open circuit not necessarily associated with a building fire, showing an abnormal condition of the normal condition of a building's FA circuitry. Specifically, these devices may be limit switches on fire water valve handles, bypass key switches for FA components, fire water line pressure switches, and the like. Troubles normally provide visual and/or audio indication at FACP's and monitoring stations but do not initiate general public notification.
Depending on the system with which you are working, ground faults in building FA wiring may show up as "troubles," or may be shown explicitly as ground faults.
I would consider communication circuits those that provide indication to offsite monitoring facilities. From memory, fire alarm systems (at least at a certain occupancy threshold) require two POT's that are monitored by a security/fire alarm company or directly by the local fire department. I mention POT's to say that these lines should/may not be routed through an on-site telephone switch or ethernet connection - they should/must be individual copper pairs (been awhile since I've commissioned a fire alarm system). As I recall there are exceptions allowing wireless or radio transmission of alarms and troubles to a remote station, though I can't be any more specific as to these requirements.
Please bear in mind this is from an installation standpoint and not from specific interpretation of NFPA 72. Did you have a more specific question regarding certain devices?
