In the banking industry most of the time "real time" means the opposite of "end-of-day".
Because there was no such thing as internet/intranet/LANs/WANs in the old days, all balancing is done at "end-of-day". Transactions done in one branch with a certain bank account are oblivious of the transactions done in another; all of the balance resolution will occur during end of day. When mainframes came in the same rule applied: resolutions are done by computer by a long-running-process usually run between 9PM and 12 midnight.
This is the reason behind terms such as "current balance" and "available balance", e.g., available balance is what has been determined by the end-of-day process as an account's balance for the previous day; current balance is what it's supposed to be, but you can't touch it yet since the bank is not sure if you've made some transaction somewhere else.
With the advent of ATMs, the internet, and other interconnectivity technologies, "real time" balance resolution is now possible: a withdrawal, an online transaction, a purchase debit, etc will immediately be reflected in the customers' bank accounts without the need to wait for end-of-day processing.