I'm not sure how that works in ether, if you have a link that would be nice to understand what you mean.

As the release manager of Bitcoin Classic we intend to release a different client under a slightly different name (classic-uahf or so) you can use to follow that chain.

As from the starting date there will be two coins you should choose which one you like. Your Bitcoins will be available on both.

If you want to follow both for some reason, then you would need to have two clients running with each using their own database directory.