BGP - Next Hop Address Tracking vs Route Dampening
Both the BGP Next Hop Address Tracking and the route dampening features use a dampening mechanism to avoid flapping and network instabilities. However, their dampening mechanisms are different and each is used for a different purpose.
The next hop tracking feature is designed to mitigate against routing instabilities resulting from a flapping next hop IP address. That is, the IGP being used continuously installs and uninstalls the next hop IPv4 or IPv6 in the routing table. When that happens, the frequency with which the next hop scanning occurs is dampened. The parameters of this dampening are hardwired and cannot be changed.
BGP route dampening however, is a different feature. This is used to mitigate against instabilities resulting from the installation and uninstallation of a BGP route. Every time this happens, a BGP update is sent, and this update has to be processed and responded to by BGP peers. This can cause disruption and instability in a BGP topology. BGP route dampening is involved in maintaining network stability when there is such an instability in the topology. The parameters of this dampening can be configured and fine tuned as needed.
The difference between the two is somewhat nuanced, but each feature deals with a different aspect of BGP.