When you use a balance sheet or a ledger you also register discrete amounts that add up to balances when you do the math. In the blockchain there are only transactions registered, not balances, but there is nothing tangible in this chain of ownership for them to be compared to a token that can be kept in a digital wallet/file. They are just values correspondent to previous transactions, existing in the cloud, but you cannot in any sense keep them in a digital file, or use it in any way that could be thought of "as sending coins by email". That doesn't exist!
It is much better to think of them as balances, and forget about those internals that make the units look like elctronic tokens and numbers.
It doesn't surprise me that people keep utterly confused about it, because you use the complexity of it to mystify it with obscurantism instead of showing the simplicity of it, that lies in keeping the private keys that contain the correspondent bitcoin address but that cannot be guessed solely with it.