According to the provided context, when a banker collects bills and credits the account, this represents a direct collection received by the bank on behalf of the customer. The context states: 'Direct collections received by the bank on behalf of the customers would increase the balance as per the bank passbook when compared to the balance as per the cash book.' When the balance increases in the passbook during an overdraft situation, the overdraft amount reduces or becomes less. Additionally, the context mentions: 'Overdraft as per the passbook is less than the overdraft as per cash book when there are cheques deposited but not collected by the banker.' Since the banker has collected and credited the bills, the passbook overdraft shows a less balance compared to what would appear in the cash book (which hasn't yet recorded this collection).