Alarm functions can work in a number of ways.
If the phone has a Calendar feature, the Alarm feature may be integrated with that, so an alarm is simply a Calendar event. Although some phones with a Calendar feature also have a separate Alarm feature.
Phones with a standalone Alarm function may allow only one alarm to be set, or may allow three or more. Most allow alarms to be set to go off once, or on a recurring basis, such as daily or weekly.
Some phones require that the phone be turned on for the alarm to work, while others will sound an alarm even while otherwise powered off.