They are separate. Theoretically, you could decommission all cash in the world and convert it into a ledger form by handing it in to the central bank and getting digital ledger money in its place within a personal account at the central bank. The central bank does not allow ordinary people to get accounts though — they do, however, allow commercial banks to do that…

Theoretically too, you could take all your normal commercial bank digital ledger money that you have in your bank account, and turn it into a non-state ‘cash’ form — if you were banking with HSBC you would get an HSBC note that could be passed around. Indeed, in the past banks actually did this, until paper money issuance was monopolised by central banks

In other words, any one discreet monetary unit can be represented either in the form of a transferable note, or as a ledger entry, but not both at once

If you want to see how this system expresses itself on the Bank of England balance sheet, check out this link http://www.bankofengland.co.uk/markets/PublishingImages/images/balance_sheet_liabilities.gif The ‘reserve balances’ are digital state e-money that the banks have access to in their central bank reserve accounts (i.e. this is a ledger form of money only accessible to commercial banks), and then the ‘notes in circulation’ are paper money that we can get hold of