Good points. A better analogy might be switching an entire LAN from token-ring to ethernet. The LAN is identical, despite the fact that the new network is incompatible with the old.
The nodes in 1982 and 1983 were largely the same, so if you look at the internet as the nodes, then there is continuity, but if you look at the internet as compatible intercommunicating protocols, then there is not.
The human side might help. The point where the actual network of connected hardware actually started to affect human society. All of the key ingredients for what is around today, but not necessarily the same hardware and software - because that has changed dramatically but not the scope of the problem space.
The nodes in 1982 and 1983 were largely the same, so if you look at the internet as the nodes, then there is continuity, but if you look at the internet as compatible intercommunicating protocols, then there is not.