There's always a separate chain when a hard fork occurs. This is why there is always so much concern about splitting the network. Because, by definition, hard forks split the network.

If you have a highly centralized system, where participants basically change consensus rules on a few days notice if Vitalik Buterin says so, hard forking without splitting the network is possible. Not so easy in Bitcoin, especially on a 3-month timeline. Most people don't upgrade their nodes on that timeline, and we can see by observing the network that the vast majority of reachable nodes are not running 2x software.