Task is a general all-encompassing term here as well as the internal task tracking tool everyone uses (called "Tasks").

Tasks could be filed by users of your service or external reports that get routed to your oncall or an alarm that fires because a metric moves outside of a "normal" range or whatever. Alarms ("pages") will come to you and need to be ACKed. Often they'll also generate a task. That task may require separate action or not. Many times those will just get closed or merged to existing tasks.