I envision a bookkeeper as a person employed by a smaller company and being responsible for recording nearly all of its transactions. Hence, the bookkeeper would likely process sales invoices, customers' remittances, purchases, payments to vendors, payroll, monitoring receivables, preparing journal entries, and more.
I view an accounting clerk as a person employed by a larger company and having a more specialized role. For example, a large company may employ one or more accounts payable clerks to process a large volume of purchases and payments. The company may also employ a payroll clerk to process its many employees' pay and fringe benefits. Perhaps an accounts receivable clerk will be employed to focus solely on the company's credit customers. A manufacturer may employ a cost accounting clerk to prepare price quotes and to monitor production information.