Only if the smoke detector trips again during this period the alarm will sound. This feature helps reduce false alarms cause by insects or dust entering the detector. You may choose either or both. Even if your system is monitored, you can even have an audible hold-up that does not send a signal to the monitoring location. The only difference is the action that the monitoring company takes when it receives the signals.
Supervisory devices can be water or gas detectors, low temperature and the like.
Normally these devices are active 24 hours a day and when tripped they do not cause the sounders to sound. They will annunciate at the command center and send a signal to the monitoring location. I have connected my outside speakers, storage shed, and pool alarm as supervisory zones. Today's control allow many levels of arming. It is used when everyone is leaving the home.