What is the difference between Tracking Stats and Campaign Reports?

Tracking Stats are just event counters that give you an overview of what is happening to your email. You can see all of the events that are occurring but the only other dimensions are domain and tag. Campaign reports have other dimensions like recipient domain and time and give you a more in-depth analysis of what is happening with your emails. In order to group emails for campaigns, you need to use the X-Campaign-Id header tag.