Accounting is record keeping. You match debits and credits, assets against liabilities and shareholder's equity. It shows cashflow, accounts payable and receivable, depreciation, inventory methods (FIFO, LIFO), and basically just tracks the money in the corporation and where it goes.
Finance has a lot of analysis. You look at different types of investments and compare them using formulas. You determine how changes in policy will affect earnings. It also deals how to obtain finances (banks, real estate, etc..) and how the company invests what is left over. Companies use accounting information in order to make financial forecasts on how their company is doing and how changes in money handling will affect its financial standing.