Hardfork has nothing to do with switching chains, it will continue on the same chain but with new rules.
Therefore the nodes running with old wallet software, and blocks mined by them after the fork are not valid on the new chain.
Here is a picture for the reference, for you to have a better understanding:



Edit: by switching chains i mean starting a completely new chain  from the scratch, and therefore old coins disappearing which does not happen with hardfork, since the old blocks will still remain.