I’ve worked in companies that used ‘tender reconciliation’ and ‘cash report’ as terms for the end-of-the-day reports.
‘Cashing out’ would be the activity that leads to those records.
A cash register can also be ‘counted down’ to the original starting sum. (As you know, a cashier never begins a shift with a completely empty register.)
The activity of running a cash register can be called ‘cashiering’.
[color=blue]By the way, have you done away with the quote button at the bottom of each post in a thread?
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