Before I provide a distinction, you should be aware that some people use the words interchangeably. Even though I was the accountant, treasurer, and CFO of a company, the owner introduced me to a group of business leaders as the bookkeeper. He knew I kept the company's books, so "bookkeeper" made sense to him. (Later, I tried to explain to him that he should not introduce me as the bookkeeper...after all I was an accountant with an MBA and CPA.)
Generally, a bookkeeper is a person without a college degree in accounting who performs much of the data entry tasks. This includes entering the bills from vendors, paying bills, processing payroll data, preparing sales invoices, mailing statements to customers, etc.
The accountant is likely to have a college degree with a major in accounting and takes over where the bookkeeper leaves off. The accountant will prepare adjusting entries to record expenses that occurred but are not yet entered by the bookkeeper. (Examples include interest on bank loans since the last loan payment, wages earned by employees that will be processed next week, etc.) Other adjustments to accounts include the calculation and recording of depreciation, establishing allowances for uncollectible accounts, etc.). After making the adjusting entries, the accountant prepares the company's financial statements (income statement, balance sheet, statement of cash flows.) The accountant also assists the company's management to understand the financial impact of its past and future decisions.
The distinction between accountant and bookkeeper keeps changing as accounting software and other software evolves. For many years, companies used the title of accounting clerks for employees doing the tasks formerly performed by bookkeepers. The accounting clerks are usually supervised by an accountant.