Customer Balance Detail vs Transaction List by Customer report
Transaction List = everything that has the Customer Name on it, such as Invoices, Payments, Sales Receipts, and even Checks you wrote with them as Payee. This is an Activities perspective; not AR, not sales, not anything financial. It should be the same Transaction listing you see when you click on their Customer Name, but a report is easy to browse, set a date range, etc.
Customer Balance Detail = only their AR activities, and it is not reliant on Open Balance. That is the same info but different perspectives, to see everything, even if they end at 0; or to see only Open, Unpaid and Unapplied AR transactions.