I am trying to understand better what happened technically with the Bitcoin Cash SV (BCH-SV) split.

What is puzzling me is that I recently created a Bitcoin Cash (BCH) wallet with an old private key which had bitcoin at the time of the BCH split in 2017. It showed the balance of BCH, which I then sent to another bitcoin cash address in a different wallet (wallet #2).

Now when I try and load that old key into a BCH-SV wallet, it shows the movement of the BCH and says that there is no BCH-SV balance available.

When I import from wallet #2 into a new BCH-SV wallet, is says that I can split the BCH-SV off.

I am not understanding what is happening here in terms of the blockchains. Why would a transfer of the BCH at a date after the BCH-SV split in 2018 result in BCH-SV being available? Are they somehow marking transactions on the BCH blockchain as either BCH alone or BCH and BCH-SV being moved?