Let's start with definitions of each:
"Classic" notifications: Carrier events are received by Shipup, analyzed, and relayed to your customers via email notifications.
"Smart State" notifications: Smart States allow you to notify your customers and alert your support team when an expected event has NOT happened after a period of time that you define (i.e. package not yet delivered, package not yet shipped, no package attributed to an order, etc.). Their purpose is to reassure the end customer and alert your support team of something that may be going wrong.
Let's look at Smart States in greater detail: