Ok I figured it out. For the benefit of others - As far as I can tell, BitSharesX were renamed to just BitShares, so they are effectively the same thing.
Further complicating things, Bitshares 1.0 (which is what BitSharesX became) was upgraded to BitShares 2.0 and Wallet files are incompatible - looks like it is a whole new blockchain in fact.
My issue was that my backups were from 0.4.27.2 which is incompatible with the last version of the original BitShares 0.9.3.c.
So first, I had to download 0.4.27.2, import my wallet files, then install 0.9.3c on top.
Within 0.9.3c, I then had to export my private keys using the console command wallet_export_keys (see
http://docs.bitshares.eu/bitshares/migration/howto-exporting-wallet.html#bitshares-1-0-full-client)
This then gave me a json file of my keys which I could import into the new Bitshares 2.0 client, via the settings menu.
Once imported, I then had to "reclaim" my old BTS1.0, again through the settings menu.
Finally, I can see my original holding.
Hope this helps someone.