Difference between "allow notifications" toggle and dragging to "do not include"
Putting an app Do Not Include will not include notifications from that app in the Notification Center. If you do not disable the other notifications then you will still receive the notifications on the lock screen and if you are using the device, but the notifications won't remain in Notification Center. Conversely, if you disable the notifications then the app is automatically moved to Do Not Include as the app will never appear in the Notification Center if there are no notifications.