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Accounting tries to provide useful information to financial statement users.Finance is about managing risk. Businesses uses information from accounting to make business decisions. Business uses finance knowledge to manage its risk.
Accounting is about keeping track of how money flows through a business as revenues, expenses, etc. It is used in making business decisions, and also by investors in evaluating the business. Finance is the study of whether particular investments are worth making when risk, timing and alternative investments are taken into consideration. Thus, an accountant might conclude that a venture is profitable, but a finance person might nevertheless choose not to invest in the venture because, for the same level of risk and with the same time horizon, another venture would be MORE profitable, or profitable more quickly. Finance decisions rely heavily on the work of accountants, of course.
To be a bit more specific on accounting, an accountant is concerned with tracking what the sources of revenues and costs are, as well as what the various assets it owns are used for. Most businesses are fairly complicated, and generate revenues and costs in all sorts of ways. A product that requires after-sales support will generate revenues both from the original sale and from the support. The cost of the HR department will be incurred by the company as a whole, but not by any specific one of its revenue-generating businesses. An accountant tries to match up the revenues and costs to the company's various activities, and tries to determine which assets (the investment in buildings, machines) are required for each activity also. This allows the accountant to look at whether the revenues generated by each activity exceed the costs of that activity or not (profitable or not?) and to look at the return generated on the investment in assets required for the activity (profits / assets). These are key inputs in business decisions, and are used - along with finance-type thinking - to decide whether to invest in starting, or expanding a business activity.
As a basic answer, financial accounting deals with the income and expenses of a company. The external reporting is done under the auspices of GAAP for tax, banking, and other external functions. Reports are strictly formatted to allow for comparative analysis. Managerial accounting is the internal reporting of how the income and expenses drive the company. There are no mandated reports and they can be in whatever format is easiest for the management team to use them. The historical data is used for forecasting, budgeting, bonuses, and a host of other needs. Hope this helps