With Pause, all of the rule's subscriptions and schedules remain intact. When a trigger fires or a scheduled event happens, the rule discovers that it is paused, and exits. The rule can be resumed by another rule or through the UI for the rule.
With Stop, all of the rule's subscriptions and schedules are removed. The rule has to be restarted through the UI for the rule. It is as if the rule was never initialized to begin with.
