Hello Robert
Yes, that is indeed correct. Classification uses either the info in the headers (using ACLs) or payload inspection (using NBAR) to determine what kind of packet (VoIP, video, web, FTP, email, etc…) each one is. Classification is essentially used to identify the application from which packets are sent. Classification is locally significant and is not communicated to any other network device.
Marking changes the ToS in the header of the IP packet and/or the CoS in the tag of the Ethernet frame. Marking can be used to communicate to devices downstream about how to prioritize such traffic based on predefined agreements. Classification is used to mark packets/frames appropriately.
Once marked, network devices can be configured to act upon the markings based on predefined QoS mechanisms, including queuing, policing, shaping, congestion avoidance, and others.
I hope this has been helpful!
Laz