Right. Who cares?
The bank of course, so they have transactions properly implemented (we must hope).
In the UK at least, such processes work entirely in the bank's favour. Transaction 1 - the money is taken from the source account, and inserted into the bank's own funds. Transaction 2 - anything from a few minutes to a few days later, if you're lucky, the money is then taken from the bank and inserted into the destination account.
That ceased to be true quite some time ago. In the days when there wasn't much computerisation, money or credit transfer between different banks, or even different branches of the same bank, was by moving pieces of paper and that couldn't be done as a single operation. By the mid 90s, at least for every bank I had dealings with, transfer between two accounts with the same bank was done as a single (distributed) transaction - money into one account and out of another, no staging through the bank's own funds; so for example I could trasfer funds from my account in Bristol to my son's account in Edinburgh by dropping in to a branch in Manchester and asking a teller to do it for me, and would be given confirmation that the money was in my son's account instantaneously (I actually did that more than once). With the new fast payment system, which has been in operation for a few years now, transfers between accounts in different banks are very fast too, but I don't know whether they are a single transaction or not (I think not). If your banks isn't using FPS, and is still taking days with the money in neither account to move money, maybe you should change to one that is.