Accounting is the professional study of business. It incorporates a heavy emphasis on compliance (tax, corporate registry etc.), for which it is best known, but also transverses management, forecasting, structuring, reporting, auditing etc. It is based heavily on legislation and precedent (corporate law, tax law, associated standards and regulations, trade practices etc.).
Finance, predominantly, relates to sources and uses of money (or capital). It is based much more on economics (particularly market economics) and has a heavy focus on "products". Capital raising, debt funding (long term, short term, secured etc.), hedging and investing (mergers, acquisitions, bonds, commercial paper etc.).