Work flow rules are to automate your business process when certain conditions of the incoming request are met. Using workflow rules, you can set e-mail alerts, assign tasks and provide assignment values to the various fields of the incoming request. When a Rule is triggered, the alerts and tasks associated to the rule are also triggered. If you do not associated any Alert or Task to the rule, the alert or task is not triggered. Hence, all the Rules, Alerts and Tasks needs to be associated with each other to work.
Notification Rules are to send notification mails to customer contacts or support reps when a new request or task are created. Also, the notification is sent to users about a contract that is going to end.