Even simpler analogy to work from: you have a file which has your list of things you bought and sold. The file is called 'transactions.txt' You make a copy of that file, calling it 'transactions_2.txt' and then start appending what you bought and sold on that. But then, you are also still appending to the old file what you bought and sold.
The Bitcoin/BCH thing is like this, but on a greater scale with potential risks around it (BCH had to ensure there were no replay attacks on the Bitcoin blockchain for example.) For example, Trezor recommends (and has to deliver your Bitcoin to a Bcash-specific address: https://trezor.io/claim-bch/.
Yes, and am I correct in assuming that once the transactions.txt is copied to transactions2.txt, they are same only till that point of time (or block), and can have totally independent and different entries from that point onwards?
If copy was made at block 55, 55th block is same in both branches. 56th and such blocks can be totally different. Imagine it like a literal branch of tree. Both branches share the same trunk, but are unique once seperated into unique branches.
The Bitcoin/BCH thing is like this, but on a greater scale with potential risks around it (BCH had to ensure there were no replay attacks on the Bitcoin blockchain for example.) For example, Trezor recommends (and has to deliver your Bitcoin to a Bcash-specific address: https://trezor.io/claim-bch/.