Hello Michael
Convergence is the state that a topology of switches achieves as a result of going through the STP processes and mechanisms to reach a stable spanning-tree topology. Convergence takes place both at the time of the initial connection of the network, as well as when the topology changes. Any event that causes a change in topology, will inevitably also cause STP to attempt to achieve convergence once again. So both situations that you describe are considered convergence.
There is a difference between detecting a change and sending out TCNs. RSTP will detect a failed link, and when that happens, a switch will immediately attempt to reconverge. This means that if a switch’s root port fails for example, it will begin the process of determining a new root port. During that process, one or more blocked ports on that switch will transition to forwarding (to replace the connectivity lost with the initial failure).
BUT, during this procedure, it will not send out a TCN at the time of failure, but at the time when the blocked port becomes a forwarding port. Only then will the TCN be sent out to all other switches in order for them to flush their MAC address tables etc… Why? Because the purpose of a TCN is to prevent MAC address tables from having incorrect entries. RSTP uses all its rapid convergence mechanisms to prevent bridging loops from forming. Therefore, topology changes are detected only so that the bridging tables can be updated and corrected as hosts appear first on a failed port and then on a different functioning port.
Take a look at this post:
I hope this has been helpful!
Laz